Biostats SDS 328M Homework 7 | Complete Solution

Biostats SDS 328M Homework 7

Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your
name and your lab time.
Round all answers to at least 3 decimal places and assume, unless otherwise noted, that α=0.05

1. A study compared the impact of pollution on two different rivers by measuring the diversity of species in each river’s floodplain. The researchers randomly selected eight 50x20 meter plots along each river and recorded the total number of species of plants in each plot, as shown below:
Alamosa River Navajo River
9 14
6 16
8 26
15 23
7 18
4 7
12 11
10 21
Carry out the appropriate test to determine if the number of plant species differs in the floodplains of these two rivers. Include all steps for full credit. (5pt)

2. Suppose that every morning, you swim 10 lengths of the outdoor lap pool in Gregory. You decide to keep track of the time it takes you to complete your swim as well as your pulse rate just after you get out of the water for a random sample of 15 different days. You confirmed all relevant assumptions were met:
Time (minutes) Pulse (beats/min)
Mean 13.60 140.08
St. Dev. 1.75 15.13
𝑟 = −0.78
a. Calculate the linear regression equation that predicts pulse rate from the time spent swimming. Show all of your work and any formulas you use. (3pt)
b. Interpret the value of the slope, in the context of the problem. (1pt)
c. If it took you 15 minutes to swim 10 pool lengths this morning, what would you predict your pulse rate to be after you get out of the pool? (1pt)
d. Does time spent swimming significantly explain variation in pulse rate? Include all steps for full credit. (4pt)

3. Forced vital capacity (FVC) is the maximum amount of air a person can expel in one breath and is an indicator of lung function. A study was conducted to test the immediate effects of exercise on FVC with a sample of 24 adult women in good health. For each of the following scenarios, name the appropriate statistical test you should run and write the appropriate null hypothesis: (2pt each)
a. The subjects were randomly divided into two groups. One group was assigned to jog on a treadmill for 30 minutes while the other group participated in a 30-minute yoga session. The FVC (in liters) of all participants was measured afterwards and you want to compare the FVC after the two different exercises.
b. The subjects were randomly divided into two groups. One group was assigned to jog on a treadmill for 30 minutes while the other group participated in a 30-minute yoga session. The change in FCV for each participant (after the workout minus before the workout) was recorded as either “increase,” “decrease,” or “stayed the same,” and you want to compare the changes in FVC after the two different exercises.
c. They measured the FVC (in liters) of each subject in the morning and then they all participated in exercise classes throughout the day. At the end of the day, the FVC (in liters) was measured again, and you want to see if there is an average change in FVC. The Shapiro-Wilk test resulted in a p-value = 0.12 .