Unit 4: Inference for Quantitative Data: Means
Statistics · Unit 4 · Paper 1

Inference for Quantitative Data: Means unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 36 terms and is the same for everyone, so a teacher can assign “Unit 4, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 32 min 29 points0/17 attempted
1

One-sample t-test statistic

2

Reporting degrees of freedom

3

Robustness of t procedures

4

One-sample t statistic

5

One-sample t-interval

6

Reading a t-table

7

How robust t procedures actually are

8

Two-sample t-interval

9

Deciding one-sample or two-sample

10

Confidence interval for a difference of means

11

One-sided p-value from two-sided output

12

Interpreting a t-interval for a difference

Short answer 1. Define or explain: Why paired designs need fewer subjects

3 pts

Short answer 2. Define or explain: Standard error of a difference of means

3 pts

Short answer 3. Define or explain: Degrees of freedom, two samples

3 pts

Short answer 4. Define or explain: Paired or two-sample?

3 pts

Free response

5 pts

A physical therapist wants to know whether a six-week stretching program increases flexibility. Twelve patients had their sit-and-reach distance, in centimeters, measured before the program and again after it. For each patient the therapist computed the difference (after − before). The twelve differences had a mean of 4.6 cm and a standard deviation of 3.2 cm. A dotplot of the differences shows no strong skewness and no outliers.

A. Explain why a two-sample t-procedure would not be appropriate for these data, and identify the procedure that is appropriate.

B. Construct a 95 percent confidence interval for the mean difference in sit-and-reach distance.

C. Interpret your interval in context, and explain what it indicates about whether the program increases flexibility.

D. Explain one reason why this study, even with a statistically significant result, does not establish that the stretching program caused the improvement.