Question

1 point) A recent study in the Journal of the American Medical Association reported the results of an experiment where 40 overweight individuals followed the Weight Watchers diet for one year. Their weight changes at the end of the year had a mean of x¯=3.1x¯=3.1 kg with a standard deviation of s=5.1s=5.1 kg. We want to use this data to test the claim that the diet has an effect, that is, that the weight change is higher than 0.

1. Which set of hypotheses should be used for testing this claim?
A. H0:μ=0H0:μ=0 vs. Ha:μ>0Ha:μ>0
B. H0:μ=0H0:μ=0 vs. Ha:μ≠0Ha:μ≠0
C. H0:μ=0H0:μ=0 vs. Ha:μ<0Ha:μ<0
D. H0:μ=3.1H0:μ=3.1 vs. Ha:μ>3.1Ha:μ>3.1

2. Which of the following conditions must be met for the hypothesis test to be valid? Check all that apply.

A. There must be at least 5 people who followed the diet for a full year.
B. The sample size must be at least 30 or the population data for weight loss must be normally distributed.
C. The amount each person's weight changed must be independent of the amount other participant's weights changed.
D. The weight loss measurements for people in the sample must be normally distributed.
E. There must be at least 10 people who 'succeeded' on the diet and 10 who 'failed'.

3. Calculate the test statistic:

4. Calculate the p-value:

5. Calculate the effect size, Cohen's dd, for this test: d^=d^=

6. The results of this test indicate we have a...
A. small
B. small to moderate
C. moderate to large
D. large
effect size, and...
A. some evidence
B. extremely strong evidence
C. strong evidence
D. very strong evidence
E. little evidence
that the observed result is not due to chance, assuming the null model is true.

6. A 95% confidence interval for the mean weight change (in kg) for people on this diet is (1.47, 4.73). Which of the statements below is correct?
A. We can be 95% confident that the mean weight loss for the population of people for whom the sample participants are a representative sample is between 1.47 kg and 4.73 kg.
B. We can be confident that 95% of the individuals who follow this diet for one year will lose between 1.47 kg and 4.73 kg.
C. There is a 95% chance that 95% of the individuals in the study who followed the diet for one year lost at least 1.47 kg.

Answer 1

1) option A

2) B. The sample size must be at least 30 or the population data for weight loss must be normally distributed.

C. The amount each person's weight changed must be independent of the amount other participant's weights changed.

3)

test statistic          t              =

(x-μ)*√n/sx=

3.8443

4)

p value                                 =

0.0002

5)

Cohen's d=|μ-μo|/σ =

0.6078

6)C. moderate to large

B. extremely strong evidence

7)

A. We can be 95% confident that the mean weight loss for the population of people for whom the sample participants are a representative sample is between 1.47 kg and 4.73 kg.