Stats Exam 3 Practice Test – Flashcards
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Fill in the blank: The t-distribution with 8 degrees of freedom has ____________________ the standard Normal distribution. A. the same center but is more spread out than B. the same center but is less spread out than C. the same center and spread as D. a different center and a different spread than
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A
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We use a t-distribution with n -1 degrees of freedom rather than the standard normal distribution whenever A. the Central Limit Theorem does not apply. B. we are using s to estimate σ. C. the population is not Normally distributed. D. we can apply the Law of Large numbers and do not need normality.
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b
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When analyzing data from a matched pairs experiment where measurements were taken on each individual before and after the treatment, we always analyze A. the mean of the before measurements minus the mean of the after measurements. B. the variability of the effect of the treatment from individual to individual. C. the correlation between the before measurements and the after measurements. D. the differences: for each individual where each difference equals the before measurement minus the after measurement. E. the variation of the before measurements and the after measurements.
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d
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Fill in the blank: The t-distribution with 4 degrees of freedom is ___________________ the standard Normal distribution. A. flatter and more spread out than B. taller and skinnier than C. the same as D. shaped the same as but has a different center than
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a
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Standard error of x-bar refers to A. the amount an observed statistic for x-bar differs from its parameter, μ. B. the estimate of the standard deviation of the sampling distribution of x-bar . C. the number of standard deviations that the observed statistic, x-bar , differs from its parameter, μ. D. the maximum amount that a statistic, x-bar , differs from its parameter, μ.
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b
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Fill in the blank: Standard error of x-bar measures ___________ of the sampling distribution of x-bar. A. shape B. center C. spread or variability
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c
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The test statistic t=(x-bar - μ)/(s/root(n)) tells us A. the maximum distance between the observed x-bar and the claimed parameter value μ0. B. how many standard errors the observed x-bar is from the claimed parameter value μ0. C. the variability of the sample x-bar 's about the claimed parameter value μ0. D. the total number of standard deviations, or σ , units x-bar is from the claimed parameter value μ0.
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b
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Whenever performing a one sample t procedure on means, we should check for A. SRS and no outliers or strong skewness in the data. B. random allocation of individuals to treatments C. only SRS. D. SRS and whether we sampled enough of the population.
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a
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Find a 95% confidence interval for μ when n = 9, x-bar = 103.14 and s = 5.25. A. (99.10, 107.18) B. (99.71, 106.57) C. (101.39, 104.89) D. (101.79, 104.49)
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a-must use t
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Suppose we were to test the hypotheses H0:μ= 80 versus Ha: μ< 80 and computed the standardized value of the test statistic to be t = -2.67 from the sample results of a sample of size n = 22. Using the t table, what is the P-value? A. 0.025 < P < 0.05 B. 0.02 < P < 0.025 C. 0.01 < P < 0.02 D. 0.005 < P < 0.01 E. Cannot find using the t table since the t test statistic value is negative.
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d
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If we fail to reject the null hypothesis, we could be making A. a type I error. B. a type II error. C. either a type I or a type II error. D. no error. An error is only made when we accidentally reject the null hypothesis.
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b
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Sample results are said to be statistically significant whenever A. the difference between the observed statistic and the claimed parameter value given in H0 is too large to be due to chance. B. the difference between the true situation and the observed situation could plausibly have resulted because H0 is false. C. the researcher subjectively classifies the observed deviation from what was expected under H0 as large enough to matter. D. the difference between the observed statistic and the claimed parameter value is large enough to be worth reporting.
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a
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See #13 on pdf
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b
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Refer to question 13. Suppose the test statistic is -1.87 (not the correct value). What is the P-value for a one-sided test? A. between 0.01 and 0.02 B. between 0.025 and 0.05 C. between 0.05 and 0.10 D. between 0.90 and 0.95 E. between 0.95 and 0.975
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c
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Refer to question 13. Suppose the P-value is really 0.305. What can we conclude at α = 0.05? A. On average students improve their score the second time. B. There is insufficient evidence to conclude that students improve their score the second time on average. C. On average students score the same each time they take the ACT exam
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b
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See #16 on pdf
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a
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A study was conducted on all small electrical appliances to determine whether any link could be found between leukemia and appliance use. Statistically significant links were found between only hair dryers and black-and-white televisions even though over 50 appliances were tested. Wise consumers of statistical information would conclude that A. there is strong evidence that hair dryers and black-and-white televisions cause leukemia. B. a difference between incidence of leukemia for those using either of the two appliances and those not using the appliances as large or larger than that observed is unlikely to be due to chance. C. while these results may be statistically significant, they are not necessarily practically significant. D. because multiple tests were performed, the results are only suggestive, not conclusive.
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d-multiple analyses increase the chance of committing a type I error
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When using a confidence interval to perform a two-sided test, H0 will be rejected whenever A. the claimed parameter value in H0 falls inside the confidence interval. B. the observed statistic value from the sample falls inside the confidence interval. C. the claimed parameter value in H0 falls outside the confidence interval. D. the observed statistic value from the sample falls outside the confidence interval.
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c
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Suppose you are testing the following hypotheses. What is the type I error for these hypotheses? H0: Cake is not done versus Ha: Cake is done A. To believe that the cake is not done when it is still not done. B. To believe that the cake is not done when it really is done. C. To believe that the cake is done when it is still not done. D. To believe that the cake is done when it really is done.
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c
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The margin of error in a confidence interval covers only which kind of errors? A. interviewer errors B. errors due to random sampling C. bias errors due to wording of questions D. computational errors
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b
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In 1990, the average cost of a normal pregnancy and delivery was $4334. Data was collected recently on a random sample of 29 recent births in a particular state. A 90% confidence interval was computed to be ($4663, $4787). On the basis of this interval, can we say that the average cost in that particular state is different from the average cost of $4334? Why or why not? A. Yes, because $4,334 is outside the confidence interval. B. Yes, because the mean for the sample of 29 births is $4,725 and that is larger than $4,334. C. No, because $4,334 is a possible value for the parameter when the sample mean is $4,725. D. No, because a sample of 29 is not a large enough sample from which we can draw inferences.
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a
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The purpose of a confidence interval is to provide A. information about the range of data in a distribution. B. a measure of the confidence we can have in our sample results representing the population. C. a list of all possible values of the statistic from all possible samples. D. plausible values that a parameter could be.
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d
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The weekly oral dosage of anabolic steroids was measured on a sample of 20 body builders. A 95% confidence interval estimate for the average weekly oral dose of anabolic steroids obtained from these results was 152 mg to 194 mg. Which one of the following is a correct interpretation of this confidence interval? A. There is a .95 probability that the average weekly dose of anabolic steroids used by body builders is between 152 mg. and 194 mg. B. We are 95% sure that the average weekly dose of anabolic steroids used by all body builders is between 152 mg. and 194 mg. C. We are 95% confident that the average weekly dose of anabolic steroids used by the 20 body builders is between 152 mg. and 194 mg. D. 95% of the time, the average weekly dose of anabolic steroids used by body builders is between 152 mg. and 194 mg. E. 95% of all body builders use between 152 mg. and 194 mg. of anabolic steroids per week.
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b
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The mean of the sample is 173 mg and the margin of error for the confidence interval given in the above question is 21 mg. Which one of the following is a correct interpretation of margin of error? A. 95% of the time, 173 will differ from the true average weekly oral dose by 21 mg. B. The figure given as 173 is not the exact value; 173 may fluctuate anywhere between 152 and 194. C. 95% of the sample means from all possible samples of size 20 will differ from the true average weekly oral dose by no more than 21 mg. D. 95% of the time, the responses of all body builders will be within 21 mg of 173 mg.
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c-the margin of error is the amount of variation that we allow in our estimate due to random sampling.
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The confidence level of the confidence interval given in question 25 is 95%. Which of the following is a correct interpretation of 95% confidence? A. There is a 0.95 probability that the average weekly oral dose of anabolic steroids is somewhere between 152 mg. to 194 mg. B. Ninety-five percent of the time, the average weekly oral dose of anabolic steroids is somewhere between 152 mg. to 194 mg. C. Using the same procedure as was used to obtain the computed interval, we will obtain intervals that contain the average weekly oral dose of anabolic steroids 95% of the time. D. Ninety-five percent of the weekly oral doses of anabolic steroids are somewhere between 152 mg. to 194 mg.
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c
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Suppose we are testing the hypotheses H0: μ = 850 versus the hypothesis Ha:μ > 850. For α = 0.05 and P-value = .092, what decision should be made? A. Reject H0 B. Fail to reject H0 C. Reject Ha D. Fail to reject Ha
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b- the P-value is greater than so we fail to reject H0.
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What two things do we need in order to compute margin of error for a one-sample t confidence interval for μ? A. Sample size and level of confidence. B. Level of confidence and the standard error of x-bar . C. Values for μ and σ. D. The mean and standard deviation of the sampling distribution of x-bar .
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b
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The mean weight for starting football players on a top 20 team in Division I was 105 kg in the 1988 football season. The question asked by a researcher was whether starters on non-top 20 teams weighed less than 105 kg on the average. Thirty six starting players on non-top 20 teams were randomly selected. What are the null and alternative hypotheses necessary to answer the question, "Is the mean weight for non-top 20 starters less than 105 kg?" A. H0: μ = 105 versus Ha: μ 105 C. H0: μ = 105 versus Ha: μ not= 105 D. H0: x-bar = 105 versus Ha: x 105 F. H0: x-bar = 105 versus Ha: x not= 105
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a
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We want to test the hypotheses H0: μ = 50 versus Ha: μ > 50 to determine whether a new variety of corn will yield more than 50 bushels per acre. We plan to sample 100 plots and measure yield per acre on each plot. Assuming H0 is true and that σ = 5, describe the sampling distribution of x-bar . A. Right skewed. B. Standard normal. C. Approximately normal with mean 50 and standard deviation 5. D. Approximately normal with mean 50 and standard deviation 0.5. E. Unknown because we do not know the shape of the distribution of yield of corn.
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d
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Refer to question #29: (We want to test the hypotheses H0: μ = 50 versus Ha: μ > 50 to determine whether a new variety of corn will yield more than 50 bushels per acre. We plan to sample 100 plots and measure yield per acre on each plot. Assuming H0 is true and that σ = 5) Suppose x-bar = 50.15 bushels per acre. Graphically, what represents the P-value? A. The area under the sampling distribution of x-bar curve between 50 and 50.15. B. The area under the sampling distribution of x-bar curve to the left of 50.15. C. The area under the sampling distribution of x-bar curve to the right of 50.15. D. The probability that H0 is true if x-bar = 50.15.
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c
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A quality control engineer needs to determine whether the oven temperature for a certain model is properly calibrated on average. Ten ovens are set at 300o F, and after one hour, the actual temperature will be measured. What hypotheses should be used to test whether the average temperature differs from 300o F? A. H0: μ = 300 versus Ha: μ > 300 B. H0: μ = 300 versus Ha: μ 300 E. H0: x = 300 versus Ha: x < 300 F. H0: x = 300 versus Ha: x not= 300
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c
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Statistically significant is equivalent to all of the following except one. Which one is not equivalent? A. P-value < α. B. The difference between the observed value of the statistic and the value of the parameter as given in H0 is too large to attribute to just chance variation. C. The probability of obtaining a sample statistic as extreme or more extreme than actually observed if H0 were true is too small for us to believe that H0 is correct. D. The observed statistic is inconsistent with the null hypothesis. E. The difference between an observed statistic and the true parameter value is due to chance variation.
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e
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How is level of confidence determined? A. From the confidence intervals. B. Subjectively determined by the researcher. C. The probability that the observed statistic falls in the confidence interval. D. Computed from margin of error. E. From the sample size: the larger the sample size, the larger the level of confidence.
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b
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Which hypothesis does the researcher generally want to prove? A. The null hypothesis. B. The alternative hypothesis. C. The claimed hypothesis. D. The significant hypothesis.
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b
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Level of confidence can be defined as A. the probability that a computed confidence interval contains the unknown parameter value. B. the percentage of time that the observations or measurements fall in the confidence interval. C. the probability that the observed statistic is in the confidence interval. D. the percentage of the time that the procedure will produce intervals that contains the parameter value.
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d
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A simple random sample of 1000 graduates of a university showed that 54% earn at least $40,000 per year. The margin of error is 3.15% for 95% confidence. Construct a 95% confidence interval estimate for the percentage of university graduates who earn at least $40,000 per year. A. $39,685 to $40,315 B. 50.85% to 57.15% C. 91.85% to 98.15% D. Cannot be constructed from information given.
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b
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Which hypothesis is assumed to be true until evidence is found to disprove or contradict it? A. The null hypothesis. B. The alternative hypothesis. C. The claimed hypothesis. D. The significant hypothesis.
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a
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When we compare the means from two independent samples, the appropriate statistic(s) is(are) A. x-bar(1) and x-bar(2) B. x-bar(1) + x-bar(2) C. x-bar(1) - x-bar(2) D. x-bar(1) / x-bar(2)
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c
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Suppose we have H0: μ = 30 versus Ha: μ > 30 with P-value = .032. If we decided to test H0: μ = 30 versus Ha: μ not= 30, what is the P-value for this new Ha assuming all other factors are the same? A. .016 B. .032 C. .050 D. .064
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d
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The manager of a major chain department store decided to offer a promotion to increase customers' usage of their credit cards issued by the chain. Before the promotion, credit card holders used their cards an average of 6.3 times per month. During the month of the promotion a random sample of 100 credit card holders used their cards an average of 6.8 times with a standard deviation of 2.5. For testing the hypotheses H0: μ = 6.3 versus Ha: μ > 6.3, what is the value of the standardized test statistic? A. 0.20 B. 0.50 C. 2.00 D. Impossible to determine from information given.
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c
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(The manager of a major chain department store decided to offer a promotion to increase customers' usage of their credit cards issued by the chain. Before the promotion, credit card holders used their cards an average of 6.3 times per month. During the month of the promotion a random sample of 100 credit card holders used their cards an average of 6.8 times with a standard deviation of 2.5. For testing the hypotheses H0: μ = 6.3 versus Ha: μ > 6.3) Suppose the P-value for the test described in the above question: is 0.013 (although this is not the correct value.) What is the appropriate statistical conclusion at the .05 level of significance? A. Reject H0 and conclude that the mean exceeds 6.3 times per month. B. Fail to reject H0 and conclude that the mean exceeds 6.3 times per month. C. Reject H0 and conclude that the mean does NOT exceed 6.3 times per month. D. Fail to reject H0 and conclude that credit card usage has stayed the same at 6.3 times per month on the average.
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a
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On the basis of the test of significance described in the above two questions and using P-value =0.013, do these data provide sufficient evidence to conclude that the promotion increased credit card usage on the average? A. Yes, the promotion increased credit card usage on the average. B. No, the promotion did not increase credit card usage on the average.
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a
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Which one of the following is a correct interpretation of the P-value given above in question 43? A. The probability that the null hypothesis is true is .013. B. The probability of rejecting a true null hypothesis is .013. C. The probability of obtaining a sample mean that exceeds the claimed mean value of 6.2 is .013. D. The probability of obtaining a sample mean that is as far or farther from the hypothesized mean value of 6.3 as the observed value of 6.8 is .013. E. The probability of getting a sample mean that is no more than 6.8 when the population mean is really 6.3 is .013.
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d
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Which one of the following does NOT affect margin of error for a one-sample t confidence interval for μ? (Assume that the necessary conditions are met.) A. Level of confidence B. Sample size C. Standard error of x-bar . D. Value of the parameter μ.
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d
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Which one of the following is NOT part of the definition for P-value? A. Probability that the null hypothesis is true. B. Probability of obtaining a value of the statistic. C. The value of the statistic is farther from the claimed parameter value than the observed statistic. D. The null hypothesis is assumed to be true.
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a
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Which one of the following is NOT synonymous with "Reject H0"? A. Results are statistically significant. B. P-value < α. C. Conclude Ha is correct. D. The results are due to chance.
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d
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What do we obtain from the sampling distribution of x-bar , created assuming the null hypothesis is true, in order to perform a test of hypothesis? A. Sample size. B. Level of significance or α. C. P-value. D. The value of x-bar .
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c
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Which of the following is NOT one of the conditions for using the formula x-bar +/- t*(s/root(n))? A. Data must be random. B. We must be able to compute the mean and standard deviation from sample data. C. , the standard deviation of the population, must be known D. The population distribution is Normally distributed.
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c
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Margin of error for 99% confidence tells us A. how much the measurements deviate from the unknown parameter mean. B. the most a statistic differs from the parameter for the middle 99% of all possible statistic values. C. the difference between the observed statistic and the unknown parameter value. D. how many standard deviations the observed statistic is from the unknown parameter value.
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b
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A test of significance is intended to assess A. the evidence provided by data against the alternative hypothesis in favor of the null hypothesis. B. the evidence provided by data against the null hypothesis in favor of the alternative hypothesis. C. the probability that the null hypothesis is true. D. the probability that the alternative hypothesis is true.
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b
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What is the purpose of a confidence interval? A. to measure the amount of confidence you have in your interval B. to determine the percentage of times the parameter will fall into your interval C. to estimate the value of a parameter D. to give a range of reasonable probability simulations
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c
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The radius of a wheel on a toy car is supposed to be 3/4 of an inch. If the wheel is too small or too large, the car will not roll properly. The manufacturer measures the radius in a random sample of 20 cars to determine whether the mean radius of the wheels currently being produced is different from 3/4 of an inch. Select the correct null and alternative hypothesis about μ. A. H0: μ < 3/4 in. versus Ha: μ = 3/4 in. B. H0: μ not= 3/4 in. versus Ha: μ 3/4 in. F. H0: μ = 3/4 in. versus Ha: μ < 3/4 in.
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d
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Calculate the margin of error from a random sample of 27 pigs with a mean weight of 54.3 kg and a standard deviation of s = 6.2 kg. Use 95% confidence. A. 0.22 kg. B. 0.45 kg. C. 1.13 kg. D. 2.45 kg. E. 21.48 kg.
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d
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Which one of the following is NOT a correct statement about margin of error? A. A small margin of error says that we have pinned down the parameter quite precisely. B. For fixed level of confidence, increasing the sample size, n, reduces the margin of error. C. For fixed sample size, decreasing level of confidence increases the margin of error. D. To obtain a smaller margin of error without increasing sample size, you must be willing to accept lower confidence.
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c
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If we decrease our level of confidence, keeping all else constant, our margin of error will A. decrease. B. increase. C. remain the same. D. change, but we can't predict whether it will increase or decrease.
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a
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Fill in the blank: Keeping all else constant, the sample mean of thirty measurements will have a margin of error that is the margin of error for a sample mean of three measurements. A. smaller than B. equal to C. larger than
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a
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Level of confidence can be defined as A. the probability that the computed confidence interval contains the value of the parameter B. the percentage of the time the confidence interval will contain the statistic measured. C. the percentage of the time that the confidence interval procedure will give you a confidence interval that contains the parameter value. D. a percentage between 0 and 100 that tells us how often the assumptions for the procedure are met.
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c
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Suppose you are testing H0: μ = 30 vs. Ha: μ > 30 with a sample of size n = 19 and the test statistic is t = 1.92. What is the P-value? A. 0.0192 B. 0.0274 C. 0.025 < P-value < 0.05 D. 0.05 < P-value < 0.10
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c
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The null hypothesis is a statement of A. the many possible values of the statistic. B. how well the statistic estimates the parameter to be tested. C. no effect or no change in the population parameter. D. an estimate of a population parameter.
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c
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See question #60
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b
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See question #61
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c
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See question #62
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b
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See question #63
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d
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See question #64
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f
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What does significant in the statistical sense mean? A. no difference. B. of great importance. C. that the test statistic supports the null hypothesis. D. not likely to happen just by chance if H0 were true.
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d
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Studies have shown the average life span of an adult male in the United States is 78 years. A sociologist believes that the average life span of an adult male in the state of Utah to be slightly higher. What hypotheses should he test? A. H0: μ = 78 Ha: μ not= 78 B. H0: μ = 78 Ha: μ 78 D. H0: x-bar = 78 Ha: x not= 78 E. H0: x-bar = 78 Ha: x 78
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c
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All of the following are true statements about the P-value except one. Which statement is false? A. P-value is the area in the tail (specified by Ha) of the sampling distribution defined by H0. B. The smaller the P-value, the greater the evidence for the alternative hypothesis. C. The larger the P-value, the greater the agreement between the data and H0. D. P-value is used to determine the significance level.
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d
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See question #68
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d
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Tests of significance on μ and confidence intervals for μ are based on A. sampling distribution of x-bar . B. the shape of the population distribution. C. the Law of Large Numbers. D. the language of sample designs.
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a
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The average time required to assemble a gas barbeque grill has been one hour and twenty minutes (80 minutes). An employee for the company has an idea that she thinks will shorten the time required for assembly. What hypotheses should be tested to determine whether her idea works? A. H0: μ = 80 Ha: μ not= 80 B. H0: μ = 80 Ha: μ 80 D. H0: x-bar = 80 Ha: x not= 80 E. H0: x-bar = 80 Ha: x 80
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b
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How large of a sample should you take in order to have a margin of error of 2 with a 95% confidence level when the standard deviation is 30? A. 30 B. 865 C. 864 D. 3457
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b-always round up when solving for sample size
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T/F The theoretical conditions necessary for performing a one-sample t procedure are: the sample was randomly selected and the population is Normally distributed.
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t
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T/F The standard error of x-bar is equal to s /root(n)
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t
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T/F The t-distribution gets closer and closer to the standard Normal distribution as the degrees of freedom increase.
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t
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T/F A matched-pairs test of significance is performed as a one-sample analysis on the differences within each of the pairs.
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t
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T/F Confidence intervals cannot be used to test hypotheses.
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f- CI's can be used to test hypotheses
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T/F The mean of every t-distribution is zero just like the standard Normal distribution.
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T
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T/F P-value is the probability that the null hypothesis is true.
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f-probability on statistics IF Ho is true
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T/F When we fail to reject H0, we may have made a type I error.
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f-may make type II error
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T/F A large P-value proves H0 is true.
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f-...without a census we cannot "prove" Ho is correct
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T/F Power is the probability that Ha is believed when H0 is true.
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f- power is the probability that Ho will be rejected if an alternative hypothesis is true
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T/F To assess practical significance, we examine the numerator of the test statistic and make a judgment call as to whether the difference has practical worth.
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t- the numerator of the test statistic shows the difference between your observed statistic and your expected parameter
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T/F (alpha) and (beta) are both computed assuming H0 is true.
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f- only (alpha) assumes Ho is true; (beta) assumes Ha is true
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T/F For fixed sample size, increasing (alpha) decreases (beta).
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t
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T/F If you reject the null hypothesis, you cannot make a type I error.
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f- ...CAN make a type I error
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T/F (beta) is found in the fail to reject H0 region under the curve of the sampling distribution defined by H0.
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f- ...curve defined by Ha, not Ho
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T/F For fixed (alpha), increasing sample size increases (beta).
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f- increasing sample size decreases (beta)
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T/F For fixed (alpha), increasing sample size increases power.
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t
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T/F To check the conditions for performing a matched pairs t test, we plot both sets of data and check each plot for outliers or strong skewness.
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f- check plot of differences NOT plots of both sets of data
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T/F When many tests of significance are performed on one set of data, the researcher is guilty of performing multiple analyses and inflating the overall (alpha).
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t
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T/F All statistical inferential procedures require either random sampling or random allocation.
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t
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T/F The margin of error for a 90% confidence interval is larger than the margin of error for a 99% confidence interval (all other things being equal.)
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f
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T/F Increasing the sample size from 100 to 500 decreases the margin of error for a 95% confidence interval.
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t
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T/F The researcher usually wants to "prove" that the null hypothesis is true.
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f- usually the researcher wants to "prove" that Ha is true
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T/F The null hypothesis is assumed to be true until the data via P-value provide evidence against it.
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t
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T/F A large (> (alpha)) P-value "proves" that the null hypothesis is true.
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f- a large p-value only gives evidence that supports Ho
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T/F We always reject H0 if P-value < (alpha).
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t
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T/F Results of a test of significance are statistically significant only if P-value < (alpha).
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t
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T/F Testing H0: μ = 80 vs. Ha: μ > 80 is a one-sided test.
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t
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T/F Testing H0: μ = 80 vs. Ha: μ not= 80 is a one-sided test.
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f- "(not =)" in Ha makes this a two-sided test t
