1. Identify whether each of the following is a matched pair or a two-sample t-test. Justify your decision.

a. A company introduces an exercise break for its workers to improve job satisfaction. They plan to conduct a survey of 100 employees before and after they implement the exercise program. They will measure job satisfaction by turning the responses into a satisfaction

the index which will be a value from 0 to 40, where 40 is the highest job satisfaction score and 0 being the poor job satisfaction score.

b. A researcher wanted to see if there is a difference in resting pulse rate for men and women. He collects a random sample of 30 men and a second random sample of 30 women and records their resting heart rate.

2. A study investigated 62 students who were randomly assigned into two equal-size groups. Group A could listen to music as they studied for a big test, while group B was not allowed to listen to music. After the exam, they calculated a 95% confidence interval for the mean difference in scores between groups, which was (-1.2, 3.4). Explain what one can conclude from this confidence interval. Does it appear that is better to study while listening to music?

3. A core mathematics project is testing an innovative approach to teaching Mathematics that emphasizes group investigations and mathematics modeling. Researchers compared 320

students who were exposed to this new approach to 273 students who learned through a traditional curriculum. Students' learning was accessed through a test at the end of the academic year to see if this new approach led to higher learning gains as compared to the traditional approach.

a. Write an appropriate hypothesis to be tested.

b. Do you think the appropriate assumptions for inference are satisfied? Explain.

c. The test results of the test are listed below, calculate the appropriate test statistic.

Program n Mean SD

Traditional 273 38.4. 18.8

New approach 320 29.0 16.2

d. Using your result from part c and 574.88 degrees of freedom. Compute the P-value.

e. Based on the P-value, what conclusion can be drawn at a 5% significance level?

4. Researchers examined the effect of phosphate supplementation on bone formation in 6 healthy adult dogs. For each dog, bone formation was measured twice: once after 12 weeks of phosphate supplementation, and once after a 12-week control period. The results in percent bone growth per year are shown below. Do these data provide evidence that phosphate supplementation significantly stimulates bone formation?

Dog ID 1 2 3. 4. 5 6

Control 1.73 3.37 3.59 2.05 1.86 3.60

Phosphate 8.16 4.58 3.98 5.24 3.04 7.03

a. an appropriate null and alternative hypothesis for the mean difference.

b. If the test statistic value was t = -2.92, determine the p-value using the appropriate degrees of freedom.

c. Based on the P-value, what conclusion can be drawn at a 5% significance level?