Multiple choice stats practice
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1. A professor gave an exam that was really easy. Most students had very high scores. A frequency polygon of the distribution of scores would most likely be an example of: a. a floor effect b. a positively skewed distribution c. a negatively skewed distribution d. both a and b
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c. a negative skewed distribution
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Bargh et al found that participants who completed a sentence-structure task with many elderly-related words (e.g. bingo, Florida, etc.) walked more slowly down a hallway compared to participants who completed a sentence-structure task without elderly related words. Bargh et al explain their effect in terms of unconscious priming. However, Doyen et al suggested that the effect may have occurred because the research assistant knew which participants were in the elderly versus non-elderly sentence-structure condition and may have inadvertently influenced participant's walking speed. These results suggest that __________ could be playing a role. a. the placebo effect b. experimenter effects or biases c. generalizability d. Hawthorne effect
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b. experimenter effect or biases
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In a normal distribution, the standard deviation is the same as the a. average of the squared deviations b. average of the absolute deviations c. average of the square root of the squared deviations d. average of the squared raw scores
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c. average of the square root of standard deviations
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In a sample of four people, Peter has a score 5 points below the mean, Amy has a score 3 points above the mean, and Chris has a score 2 points below the mean. Which of the following provides the most accurate description of the score for Jerry? a. it is equal to the mean b. it is below the mean c. it is above the mean d. more information is needed
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c. it is above the mean
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You want to study how fruit consumption affects happiness specifically in Gettysburg College students. You randomly pick 50 students from the students who are eating breakfast at Servo on a Monday morning at 8 am. You flip a coin for each student and assign heads to the fruit condition and tails to the no-fruit condition. These students then eat fruit or do not eat fruit and happiness is measured after the meal is completed. This participant sampling technique is an example of a. haphazard sampling b. random sampling c. inconvenient sampling d. none of the above--sampling only occurs when there is an unknown population
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a. haphazard sampling
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An organizational psychologist conducts extensive interviews in order to examine worker morale in a factory. She randomly selects and interviews 100 workers from the factory. In this example, what is the population? a. the 100 workers interviewed b. all workers in the factory c. all workers in the factory except the 100 interviewed d. none of the above--the term "population" only applies when there is a known normal distribution
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b. all workers in the factory
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___ is to σ as M is to μ
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SD (standard deviation)
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In a particular community, 4000 adults are married, 2000 have never been married, 2000 are divorced, and 2000 are widowed. Suppose you are conducting a survey in this community and telephoned a person at random. a. what is the probability that this person has never been married? b. what is the probability that this person would be either married or divorced?
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a. 2000/10000= .20 b. 4000/10000 + 2000/10000 = 6000/10000 = 3/5 = .60
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A researcher is interested in whether the color of an animal's surroundings affects its learning rate. She tests 31 rats in a maze box with colorful walls. It is known that the average rat of this strain can learn to run this particular type of maze in a box without any special coloring in 28 trials with a variance of 64. The mean number of trials to learn the maze for the rats tested with the colorful wallpaper is 12.50. What is the M? a. 28 b. 31 c. 12.50 d. 64 What is the shape of the distribution in the above problem? a. positively skewed b. negatively skewed c. approximately normal d. it cannot be determined from the information given
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c. 12.50 c. approximately normal
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Briefly define a distribution of sample means. Why do we use this distribution as a comparison distribution when performing hypothesis testing?
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A DOSM is the average of the means of different samples taken from the same population. This is used as a comparison distribution when performing hypothesis testing because you cannot compare the scores of a sample to the average of the total population. This would be comparing 2 different things. They aren't on the same scale. A DOSM is used because it is on the same scale as the average from a sample. You're comparing data from a sample to data from samples instead of data from a sample to data from population.
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Which of the follow statements is false about t distributions? a. t distributions generally have large tails b. there are many categories of t distributions c. the smaller the degrees of freedom, the more a t distribution resembles a normal curve d. for any given sample size, there is a different t distribution
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c. the smaller the degrees of freedom, the more a t distribution resembles a normal curve
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When calculating the variance of a DOSM based on estimated population variance, you divide the estimated population variance by ______
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N
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When estimating the population variance, why is N-1 used in the denominator?
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N-1 is used in the denominator when estimating population variance because it reduces bias of the estimated variance.
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Strack, Martin, and Stepper showed that facial expressions can affect behavior. A hypothetical researcher wonders if facial expressions can affect one's ability to solve complex math problems. The researcher randomly assigns 25 people to a smile condition and 29 people to a frown condition. The researcher then measures everybody's ability to perform math problems. The researcher finds that people who smiled completed an average of 6.12 math problems while those who frowned completed an average of 5.10 math problems. The researcher decides to perform an independent samples t-test to determine if these means are statistically significant. What is the mean of the comparison distribution in this problem? a. 0 b. 6.12 c. 5.10 d. it cannot be determined with the info given What is the comparison distribution in the above problem? a. a distribution of differences between means b. a distribution of means of differences scores c. a DOSM for a sample size of 54 d. a distribution of t scores that follows a normal curve
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a. 0 a. a distribution of differences between means
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A researcher hypothesizes that sleep deprivation will correlate with aggression. In order to test this assumption, what will be required? a. inferential statistics b. random assignment c. the measurement of a rank order variable d. both a and b
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a. inferential statistics
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In a study of living conditions at colleges researchers measure the square footage of the dorm rooms where students live. a. nominal b. rank order c. equal interval
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c. equal interval
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A credit card company assigns a rating to cardholders in terms of default risk from 1 (no risk) to 10 (high risk). a. nominal b. rank order c. equal interval
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c. equal interval
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In a survey of voter preferences, researchers characterize voters as democrat, republican, or independent. a. nominal b. rank order c. equal interval
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a. nominal
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A college examines its graduating seniors so that they can place them into a class rank in order of highest to lowest. a. nominal b. rank order c. equal interval
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b. rank order
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Explain what is meant by a ceiling effect in a distribution of scores. Give an example and list the other term we use for this type of distribution.
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The ceiling effect is when scores pile up at a distribution's high end because a higher score cannot be had, such as with a distribution of exam scores, where participants cannot score higher than 100%. This type of distribution is also called a negatively skewed distribution.
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Researchers wanted to know how much TV people watch per day. They placed video cameras in 30 homes and recorded people as they watched TV in order to determine how much TV people watched each day. The researchers were surprised to learn that people in these 30 homes only watched 1.50 hours of TV a day. Before making strong conclusions, the researchers should consider: a. random assignment b. the placebo effect c. external validity d. the Hawthorne effect
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d. the Hawthorne effect
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When conducting research, researchers can use a within-subjects or between-subjects design. First, define these two designs. Then list some advantages and disadvantages of using a within-subjects design.
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A within-subjects design is when the experimenter gives the independent variable and the placebo to the same group of people. A between subjects design is when one group of people receives the placebo and another group receives the independent variable. The disadvantages of a within-subjects design are that participants are receiving both the independent variable and the control, making it hard for the effect of the independent variable to be measured. An advantage of the within-subjects design is that you are using the same group of people, so there is less of a risk of participant variables biasing the study or affecting the results.
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Define mean in your own words (explain what it generally measures, not how to compute it).
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The mean is the average of a group of scores.
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Define median in your own words (explain what it generally measures, not how to compute it).
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The median is the number in the exact middle of the distribution when scores are arranged from low to high.
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Define standard deviation in your own words (explain what it generally measures, not how to compute it).
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The standard deviation measures, on average, how far the scores in a group differ from the mean.
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Define Z-score in your own words (explain what it generally measures, not how to compute it).
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The Z-score measures how many standard deviations a score differs from the mean. It can be used to compare scores from different data sets because it places all scores on a universal scale.
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Under what circumstances would it make sense to use the median instead of the mean as a measure of central tendency? When would it make sense to use the mode instead of the mean?
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The median should be used instead of the mean when there are extreme scores, outliers, in the distribution, such as in our class data results for the question of how much money we expected to make 10 years after graduation, where there was a very high score at one end of the distribution. The mode should be used when nominal levels of measurement are used, such as data on a group's favorite ice cream flavor.
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In a distribution of Z scores, the SD is always ___ and the M is always ___.
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SD is always 1 and the M is always 0
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Imagine that on New Years Eve, the probability of having a car accident is .01, the probability of getting stuck in traffic is .14, and the probability of having an alcoholic drink is .22. If someone asked you what the probability is of getting stuck in traffic or having a car accident, what would you need to determine the answer? a. the addition rule b. the multiplication rule c. the division rule d. both a and c
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a. the addition rule
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A social psychologist measures the amount of loneliness experienced by college students. The distribution was normal with a M of 60 (SD=6.00). a. Approximately (use approximation rules, not a table; no need to go through the steps, just list the percentage) what percent of college students have loneliness scores below 66? b. Approximately (use approximation rules, not a table; no need to go through the steps, just list the percentage) what percent of college students have loneliness scores above 72? c. In everyday language, what does it mean to say that a student's loneliness score was in the bottom 5% of the sample?
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a. 84% b. 2% c. It means that the student experienced significantly less loneliness than the average student.
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How many of the following statements are true? -The p value of a test is the probability of obtaining a result as extreme as the one obtained assuming the null hypothesis is true -The p value of a test can be less than 0 regardless of whether or not the null hypothesis is true -When the null hypothesis is rejected, one can be certain it is not true. a. 1 b. 2 c. 3 d. none of them
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a. 1
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A researcher says that based on the results of her study the null hypothesis is accepted, and that it is accepted because the probability of obtaining her result if the null hypothesis was true is greater than 1%. How would this probability statement be symbolized?
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p>0.01
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Type I error
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A type I error is when a researcher rejects a true null hypothesis. ex: Sally believes that caffeine consumption causes higher levels of alertness. After completing her study, she does hypothesis testing and gets a p value of 5.10. She rejects the null hypothesis, but her data is not statistically significant because the probability of getting this result if the null was true is not less than 5%. She has committed a type I error.
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Type II error
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A type II error is when a researcher accepts a false null hypothesis. ex: Nate believes that those who live in urban areas will score higher on a geography test than those living in rural areas. After completing his study, he does hypothesis testing and gets a p value of .047, indicating that his data is statistically significant because there is less than a 5% probability of getting this result if the null was true. However, Nate accepts the null hypothesis. He has committed a type II error.
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Did you hear the joke about the statistician who drowned while wading across a river whose average depth was three feet? What did the statistician forget to take into account? a. the median b. the standard deviation c. inferential statistics d. the mode
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b. the standard deviation
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True or False 1) When a distribution has a negative skew, the median is greater than the mode 2) Internal consistency is a measure of the reliability of a construct 3) Degrees Fahrenheit is measured on an equal interval scale
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1) False 2) True 3) True
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True or False 4) Populations are always larger than samples 5) Kurtosis is used to describe the N of a distribution 6) In terms of probability, the expected relative frequency is the number of times something happened relative to the number of times it should have happened 7) In hypothesis testing, it is more difficult to find a significant effect with a one-tailed test than a two-tailed test
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4) True 5) False 6) True 7) False
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Which of the following statements reflects the best example of the influence of outliers? a. if you want to know the correlation between height and weight in adults and examine a random sample of 200 adults b. when you calculate the correlation coefficient for 2 variables when variable x occurs before variable Y c. when you calculate the correlation coefficient for the relationship between age and shoe size and you have people in the sample from several age groups d. none of the above options
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d. none of the above options
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When high scores on one variable go with high scores on another variable and low scores on the first variable go with low scores on the second variable, the correlation coefficient will be between ____ and ____.
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0 and 1
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If every increase of 1 pt on an anxiety scale is associated with a decrease of 2 points on predicted performance on a test, the 2 is also the a. regression coefficient b. regression constant c. proportionate reduction in error d. standardized regression coefficient
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a. regression coefficient
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What does it mean when SStotal minus SSerror equals 0? a. This is the best case--it means there is 0 error b. This is the worst case--it means the prediction model has reduced 0 error c. the proportion reduction in error is exactly 50% d. the underlying correlation coefficient between X and Y is negative rather than positive
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b. This is the worst case--it means the prediction model has reduced 0 error
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The predicted score or value when the predictor variable is at zero corresponds to _____ (give a name or symbol)
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a
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In your own words, define a DOSM.
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A distribution of sample means is a distribution comprised of the averages of samples of the same size, all taken from the same population and put onto a frequency distribution.
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Why do we use a DOSM when performing hypothesis testing?
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The DOSM is used when performing hypothesis testing so that samples can be compared to a distribution of samples of the same size. If you tried to compare the mean of a sample to the mean of a population, it would be like comparing apples and oranges--they wouldn't be on the same scale. In order to compare a sample to data from the population, psychologists create the DOSM by creating samples of the same size from the same population and plotting the averages to compare samples to.
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What happens to the shape of a DOSM if the sample size increases?
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If the sample size increases, the shape of the DOSM becomes narrower, with most scores concentrated in the middle, because more scores are falling around the midpoint, just as with the normal curve. The more scores you have, the more scores that fall in the middle of the distribution making the distribution narrower. As sample size goes up, variance and standard deviation decrease, so there is less variance, thereby making the shape narrower as sample size increases.
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If the psychiatrist used a sample size of 55 rather than 45, what would happen to the standard deviation of the distribution of sample means? a. it would increase b. it would decrease c. it would stay the same d. it is not possible to predict without more information
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b. it would decrease
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Another name for σM is a. standard error of the sample b. standard deviation of the sample c. standard deviation of the population d. standard error of the mean
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d. standard error of the mean
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We learned that one should always try to report an effect size when conducting statistical analyses. One important advantage of using an estimate of effect size is that a. it tells you all of the relevant parameters of an experimenter's data set b. it is a standardized score, allowing us to compare one experiment with another experiment c. it is frequently reported as a measure of spread along with variance d. it tells us whether an experiment is statistically significant
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b. it is a standardized score, allowing us to compare one experiment with another experiment
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Define statistical power.
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Statistical power is the probability that study's results will be statistically significant if the research hypothesis is true.
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What is the relationship between power and Beta, which is the probability of making a type II error?
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To find Beta, you take 1-power of the study
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Pick which one is higher in power when all other factors are equivalent: d=.55 or d=.45 SD=6 or SD=5 N=35 or N=45 α=.01 or α=.05 Beta=.66 or Beta=.45 strong manipulation or moderate manipulation
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d=.55 SD=5 N=45 α=.05 Beta=.45 strong manipulation
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A t test for independent samples differs from an analysis of variance (ANOVA) in that a t test for independent samples a. cannot be used in most situations in which an ANOVA would be used, but an ANOVA can be used in most situations in which a t test can be used b. is usually used to compare two groups but an ANOVA is not c. it is conducted before the experiment, but an ANOVA is conducted after the experiment d. figures estimated population variance as part of the analysis but an ANOVA does not
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a. cannot be used in most situations in which an ANOVA would be used, but an ANOVA can be used in most situations in which a t test can be used
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You conduct an ANOVA comparing four groups of people on their self-esteem scores. If you reject the null hypothesis, what does this rejection tell you? a. that at least one mean is different from one or more of the other means b. that all means are significantly different from each other c. that none of the means are significantly different from each other d. none of the above are true
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a. that at least one mean is different from one or more of the other means
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If a researcher conducts 100 t tests, each at an alpha level of .05, how many t tests are likely to be significant even if the null hypothesis is true?
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5
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A social psychologist wants to examine whether the number of romantic relationships formed during the first year college differs from the number of romantic relationships formed during the final year of college. She finds a sample of 35 first year students and measures the number of romantic relationships they experience in their first year. Then she measures the same variable in 35 seniors. Determine which procedure you would use to test the hypothesis.
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t test for independent samples
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Gettysburg College conducts a study of its students in order to determine if the number of hours they study per week differs among their first and second years. They ask first year students how many hours they study and then they ask them again when they are in their second year. Determine which procedure you would use to test the hypothesis.
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t-test for paired samples (t test for dependent means)
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A social psychologist hypothesizes that the attributions people make for their own behavior differ when they are in a positive versus negative mood. He randomly assigns people to undergo either a positive mood induction or a negative mood induction. He then measures their attributions after each mood induction. Determine which procedure you would use to test the hypothesis.
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t test for independent samples
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A social psychologist hypothesizes that sleep deprivation increase aggression. She measures the aggression of 30 people who have not slept for 24 hours and compares that score to the score of two other groups, one group of 30 people who have slept for 4 hours in the last 24 hours and one group of 30 people who have slept for 8 hours in the past 24 hours. Determine which procedure you would use to test the hypothesis.
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ANOVA
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The final step in conducting an ANOVA is the calculation of an F ratio. A large F ratio suggests that we have a significant effect whereas a small F ratio suggests we do not have a significant effect. A large F ratio occurs when the _______ is much smaller than the _______.
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A large F ratio occurs when the S^2 within is much smaller than the S^2 between.
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True or False 1) Using a narrative review is a less objective way to evaluate the overall results of a study on a topic compared to a meta-analysis 2) A researcher "fishing" for results after a study typically conducts planned comparisons 3) If the F value for an ANOVA had a df of 4 in the numerator and a df of 32 in the denominator, then there were 4 groups in the study. 4) The value of F in an ANOVA is always positive 5) R^2 or eta^2 always ranges between 0 and 1.
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1) True 2) False 3) False 4) True 5) True
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Which of the following data sets should not be analyzed using a Chi-square test? a. whether the use of a particular cleaning product (yes or no) varies by a person's ethnicity b. preference for studying (sitting or lying down) is assessed in first and second year students c. Belief in God (yes or no) is assessed in people who are sad and then later when they are happy d. a person's coffee drinking preference (yes or no) is assessed in people who are sleepy and in people who are awake
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c. Belief in God (yes or no) is assessed in people who sad and then later when they are happy
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When carrying out a chi-square test for independence, a good check of your math in calculating the expected frequencies is to make sure that a. the sum of all the expected frequencies times the degrees of freedom equals the sum of all observed frequencies b. the expected frequency of each cell is no larger than the observed frequency c. for each row, the sum of all the expected frequencies equals the observed frequencies, minus 1 for each column d. within any one row or column, the sum of the observed frequencies and the sum of expected frequencies come out to be the same
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d. within any one row or column, the sum of the observed frequencies and the sum of expected frequencies come out to be the same
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Chi-square distributions are ________ skewed
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positively
