# EBook Problems Infer 2Means Indep

## EBook Problems Set - Inferences About Two Means: Independent Samples Problems

### Problem 1

A researcher wants to compare all students at Kansas State University (population = 22,000) with all residents of the city of Springfield, IL (population = 22,000). He wants to estimate the average age of each population using two separate samples. He wants the same margin of error for each of his sample means. How would the size of the two samples compare?

• Choose at least one answer.
(a) the sample sizes should be the same since the population sizes are the same.
(b) No way to tell.
(c) The KSU sample should be smaller than the Springfield sample.
(d) The KSU sample should be larger than the Springfield sample.

### Problem 2

For this research situation, decide what statistical procedure would most likely be used to answer the research question posed. Assume all assumptions have been met for using this procedure.

Does knowing a college student's SAT score tell us anything about his or her first year college grade point average?

(a) Test the difference between two means (independent samples)
(b) Test one mean against a hypothesized constant
(c) Test that a correlation coefficient is not equal to 0 correlation analysis
(d) Test the difference in means between two paried or dependent samples
(e) Use a chi-squared test of association

### Problem 3

Suppose you were hired to conduct a study to find out which of two brands of soda college students think taste better. In your study, students are given a blind taste test. They rate one brand and then rated the other, in random order. The ratings are given on a scale of 1 (awful) to 5 (delicious). Which type of test would be the best to compare these ratings?

(a) Paired difference t
(b) Chi-square
(c) One-sample t
(d) Two-sample t

### Problem 4

In a study of graduate students who took the Graduate Record Exam (GRE), the Educational Testing Service reported that for the quantitative exam, U.S. citizens ha da mean of 529 and a standard deviation of 127, whereas the non-U.S. citizens had a mean of 649 and a standard deviation of 129. Choose the best answer from the following.

(a) Both groups had about the same amount of variability in their scores, but non-U.S. citizens performed better, on the average, than U.S. citizens.
(b) A non-U.S. citizen who scored three standard deviations below the mean had a score of 200.
(c) If the scores range between 200 and 800, then probably the scores for non-U.S. citizens were symmetric and bell shaped.
(d) If the distribution of scores was approximately bell-shaped, then almost no U.S. citizens scored below 400.