ISYS 5503: CH 8 practice test

question

Suppose a researcher is interested in determining the average amount of gasoline used by a household per month. If the population standard deviation is unknown, which of the following methods could be used to determine the sample size necessary for an interval estimate of the population mean amount of gasoline if the researcher wants to be accurate to within 4 gallons with 90% confidence? a. Use a pilot study to select a preliminary sample. b. use a “best guess” method for the value of the pop StDev. c. Use an estimate of the population standard deviation from a previous or similar study. d. All of these choices.
answer

d. All of these choices. pg 360
question

A random sample of 100 metro trains showed an average delay of 5 minutes. The distribution of delay times for all trains is normally distributed, with a standard deviation of 2.1 minutes. If we are interested in determining an interval estimate for the population mean at 98% confidence, the z value to use is a. 1.96 b. 2.33 c. 0.21 d. 2.05
answer

b. 2.33
question

If we want to provide a 90% confidence interval for the mean of a population, the confidence coefficient is: a. 1.28 b. 0.84 c. 0.90 d. 1.645
answer

c. 0.90
question

What is the mean of the t distribution associated with a random sample of size 7? a. 6 b. 0 c. 1 d. It depends on the values in the data set.
answer

b. 0
question

Which of the following is a true statement? a. The t distribution is used to compute a confidence interval when pop StDev is known. b. As n becomes large the t distribution approaches a normal distribution. c. The t distribution is symmetric about 1. d. For every size sample, the t distribution has constant variance like the standard normal.
answer

b. As n becomes large the t distribution approaches a normal distribution.
question

For which of the following situations can the normal distribution be used to compute confidence interval estimates for the population proportion, p? a. it can be used when np >= 10 b. it can be used when n(1+p) >= 5 c. it can be used when p has a normal distribution d. It can be used when both np >= 5 and n(1-p) >= 5
answer

d. It can be used when both np >= 5 and n(1-p) >= 5
question

The t value with 92% confidence and 11 degrees of freedom is: a. 1.928 b. 1.751 c. 1.507 d. 1.895
answer

c. 1.507
question

A company wants to determine a 90% confidence interval estimate for the average weekly sales. Assuming that the company reports that the standard deviation of weekly sales is $175, how many weeks should they sample so that the margin of error will be $60 or less? a. 14 b. 24 c. 5 d. 33
answer

b. 24 pg 360
question

When estimating a population mean, the sample size needed to provide a margin of error of 5 or less with a .95 probability when the population standard deviation equals 13 is: a. 19 b. 15 c. 26 d. 6
answer

c. 26
question

In a random sample of 250 adults between the ages of 25 and 30, 34% say they have started saving for their retirement. Which of the following is a 90% confidence interval for the population proportion? a. .339 to .342 b. .291 to .389 c. .448 to .552 d. .281 to .399
answer

b. .291 to .389
question

Suppose the ages of four randomly selected students at a community college are recorded. 31 55 42 26 Assuming the sample was selected from a large, normally distributed population, which of the following represents a 95% confidence interval estimate for the population mean? a. 23.35 to 53.65 b. 25.76 to 51.24 c. 18.02 to 58.98 d. A confidence interval cannot be computed with the information given.
answer

c. 18.02 to 58.98
question

A local hotel wants to estimate the proportion of its guests that are families. Preliminary estimates are that 35% of the hotel guests are families. How large a sample should be taken to estimate the proportion of family guests with a confidence level of 90% and a margin of error no larger than 6%? a. 684 b. 171 c. 243 d. 35
answer

b. 171
question

A random sample of 15 items is selected from a population that is not normally distributed and whose standard deviation is not known. if xbar = 125 and sample StDev = 6, which of the following represents a 90% confidence interval estimate of the population mean? a. 122.27 to 127.73 b. 114.44 to 135.56 c. 121.68 to 128.32 d. A confidence interval cannot be computed since the population is not normal.
answer

a. 122.27 to 127.73
question

The computer output from a statistical analysis gives (0.44, 0.53) as a 99% confidence interval for the population proportion. How do you interpret this output? a. We are 99% confident that the population proportion lies in the interval (0.44, 0.53). b. There is a 95% chance that the population proportion lies in the interval (0.44, 0.53). c. We are 95% confident that the population proportion is greater than 0.44. d. We are 95% confident that the population proportion is 0.485, the midpoint of the given interval.
answer

a. We are 99% confident that the population proportion lies in the interval (0.44, 0.53).
question

What is the margin of error given the values sbar = 26.5, Pop StDev = 8.2, n = 40, z = 1.96 a. 26.5 b. 1.30 c. 2.54 d. 1.96
answer

c. 2.54
question

If we change an 80% confidence interval estimate to a 95% confidence interval estimate, we can expect the: a. width of the confidence interval to increase. b. width of the confidence interval to decrease. c. width of the confidence interval to remain the same. d. sample size to increase.
answer

a. width of the confidence interval to increase.
question

Which of the following values of p will ensure the required margin of error is satisfied when determining the sample size for an interval estimate of a population proportion? a. p = 0.90 b. p = 1.0 c. p = 0.50 d. p = 0.95
answer

c. p = 0.50
question

The test scores of five randomly selected students at a community college are given below. 85 96 72 91 80 Assuming the sample was selected from a large, normally distributed population, which of the following represents the margin of error assuming a 95% confidence level? a. 6.57 b. 8.15 c. 2.77 d. 18.22
answer

d. 18.22
question

What is the t value for t.05 and 7 degrees of freedom? a. 1.895 b. 0.05 c. 2.365 d. 1.943
answer

a. 1.895
question

A random sample of 35 items is selected from a population that is not normally distributed and whose standard deviation is not known. if xbar = 300 and Sample StDev = 80, which of the following distributions should be used to compute an interval estimate for the population mean? a. a normal distribution with a mean of 300 and a standard deviation of 80 b. a t distribution with 34 degrees of freedom c. a t distribution with 299 degrees of freedom d. a standard normal distribution
answer

b. a t distribution with 34 degrees of freedom
question

A random sample of 10 varieties of yogurt was selected. The average calories per serving for these yogurts is xbar = 90. Assuming the Pop StDev = 5, find the 95% confidence interval for the mean calories in a serving of yogurt. a. 83.4 ± 92.6 b. 88.4 ± 91.6 c. 86.9 ± 93.1 d. 89.0 ± 90.9
answer

c. 86.9 ± 93.1
question

In which of the following situations should the t distribution be used? a. when the sample size is less than 30 b. when the population is normally distributed c. when the population standard deviation is unknown d. only when the population means is 0
answer

c. when the population standard deviation is unknown
question

Which of the following values of p should be used to compute the sample size that guarantees all estimates of proportions will meet the margin of error requirement? a. .01 b. .25 c. .50 d. 1
answer

c. .50
question

The z value for a 99% confidence interval estimation is: a. 1.96 b. 2.57 c. 2.33 d. 1.96
answer

b. 2.57
question

A 90% confidence interval for a population proportion is determined to be 0.75 to 0.85. If the level of significance is decreased, the interval for the population proportion: a. becomes narrower. b. becomes wider. c. does not change. d. not enough information is provided to answer this question.
answer

b. becomes wider. Because a decreased level of significance is an increased confidence interval
question

The manager of a retail store has taken a random sample of 100 customers. The average amount spent by these 100 customers was $75. It is known that the standard deviation of the amount spent is $8.20. If the confidence coefficient is increased from .90 to .95, the standard error of the mean: a. will decrease. b. will double in size. c. will increase d. will remain unchanged.
answer

d. will remain unchanged. because the standard error is the standard deviation
question

Which of the following must be decided by the researcher when computing the minimum sample size for an interval estimate of the population mean or proportion? a. Degrees of freedom b. Standard deviation c. Margin of error d. Mean
answer

c. Margin of error
question

Which of the following is not required when computing the sample size for an interval estimate of the population mean? a. z value at alpha/2 b. Population standard deviation c. Population mean d. Margin or error the researcher is willing to accept
answer

c. Population mean
question

A university recruiter would like to determine the proportion of high school students who plan to apply for financial aid when attending college. She surveys 114 current high school seniors who plan to attend college and finds that 98 plan to apply for financial aid. Which of the following is a 95% confidence interval estimate for the proportion of students who plan to apply for financial aid? a. .7963 to .9237 b. 77 to 95 c. .50 to .75 d. .8065 to .9135
answer

a. .7963 to .9237
question

A 90% confidence interval and a 96% confidence interval are computed from the same set of data. Which of the following statements is correct? a. The intervals have the same width. b. The 90% confidence interval is wider. c. The 96% confidence interval is wider. d. You need to know the sample size, n, and the standard deviation to determine which interval is wider.
answer

c. The 96% confidence interval is wider.
question

A random sample of 10 employees was taken. The average age in the sample was 42 with a variance of 25. Assuming the ages are normally distributed, the 95% confidence interval for the population average age is: a. 38.42 to 45.58 b. 39.10 to 44.90 c. 38.90 to 45.10 d. 24.12 to 59.88
answer

a. 38.42 to 45.58
question

It is known that the variance of a population equals 169. With a .90 probability, how large of a sample would have to be taken to provide a margin of error of 10 or less? a. 5 b. 773 c. 7 d. 169
answer

a. 5
question

What sample size should be used if we would like to estimate the mean income of the residents of an apartment complex with 95% confidence? We would like to be accurate to within $2000 and we will assume the population is normally distributed with a standard deviation of $4200. a. 6 b. 17 c. 23 d. 12
answer

b. 17
question

The manager of a grocery store wants to determine the proportion of customers whose purchases include at least five products, which are store brand. What size sample should he take so that at 92% confidence the error of his estimate will not be more than 8%? a. 78 b. 120 c. 11 d. There is not enough information given to determine the sample size.
answer

b. 120

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