Question

GRADED PROBLEM SET #8

Answer each of the following questions completely. When possible to answer using a complete sentence and offering explanation, please do so. There are a total of 20 points possible in the assignment.

1. Resveratrol, an ingredient in red wine and grapes, has been shown to promote weight loss in rodents. One study investigates whether the same phenomenon holds true in primates. The grey mouse lemur, a primate, demonstrates seasonal spontaneous obesity in preparation for winter, doubling its body mass. A sample of six lemurs had their resting metabolic rate, body mass gain, food intake, and locomotor activity measured for one week prior to resveratrol supplementation (to serve as a baseline) and then the four indicators were measured again after treatment with a resveratrol supplement for four weeks. Some p-values for tests comparing the mean differences in these variables are given below. In parts a-d, state the conclusion of the test using a 5% significance level, and interpret the conclusion in context. (HINT: For thinking of the null/alternative hypothesis, the null would be that there is no change and the alternative would be what they are trying to test as described in the wording in each part)
   1. In a test to see if mean resting metabolic rate is higher after treatment, p=0.013

2. In a test to see if mean body mass gain is lower after treatment, p=0.007

3. In a test to see if mean food intake is affected by the treatment, p=0.035

4. In a test to see if locomotor activity is affected by the treatment, p=0.980

5. In which test is the strongest evidence for rejecting the null found? The weakest?

6. How do your answers to parts a-d change if the researchers make their conclusions using a stricter 1% significance level?

2. There were 2430 Major League Baseball games played in 2009, and the home team won the game in 53% of the games. If we consider the games played in 2009 as a sample of all MLB games, test to see if there is evidence, at the 5% level, that the home team wins more than half the games. (Show all steps of the hypothesis test to receive points)

Answer 1

Decision rule :

There is significant evidence to reject the null hypothesis , if p-value ≤ α

There is no significant evidence to reject the null hypothesis , if p-value > α

We are given α = 0.05

a) p value = 0.013

Since p value is less than 0.05,we reject the null hypothesis

There is significant evidence that mean resting metabolic rate is higher after treatment.

b) p value = 0.007

Since p value is less than 0.05,,we reject the null hypothesis

There is significant evidence that mean body mass gain is lower after treatment.

c) p value = 0.035

Since p value is less than 0.05, ,we reject the null hypothesis

There is significant evidence that mean food intake is affected by the treatment.

d) p value = 0.980

Since p value is less than 0.05, ,we do not reject the null hypothesis

There is no significant evidence that locomotor activity is affected by the treatment.

e) Since for the body mass gain treatment test in part b) has lowest p value , it has the strongest evidence for rejecting the null.

d) We are asked to use α = 0.01

Therefore the body mass gain treatment test in part b) is the only test that has significant evidence to reject the null ,because its p value is less than 0.01

So for α = 0.01 only body mass gain treatment test shows the significant evidence that mean body mass gain is lower after treatment.