One way to measure a persons fitness is to measure their body fat percentage. Average body fat
Question:
One way to measure a person’s fitness is to measure their body fat percentage. Average body fat percentages vary by age, but according to some guidelines, the normal range for men is 15-20% body fat, and the normal range for women is 20-25% body fat.
The body fat of 25 gym goers was measured by a trainer and the Mean and standard deviation for each group is summarized in table below.
Group | Sample Size (n) | Average (X-bar) | Standard deviation (s) |
Women | 10 | 22.29 | 5.32 |
Men | 15 | 14.95 | 6.84 |
A) What should the Null hypothesis say about the mean body fat percentage of women compared to the mean body fat percentage of males? | |
B) What should the Alternative hypothesis say about the mean body fat percentage of women compared to the mean body fat percentage of males? | |
C) Is the p-value for your test less than 0.05? "yes" or "no" | |
D) At the 0.05 significance level, is there enough evidence to conclude that the mean body fat percentage for women is more than 3% greater than men? "yes" or "no" | |
E) At the 0.01 significance level, is there enough evidence to conclude that the mean body fat percentage for women is more than 3% greater than men? "yes" or "no" | |
F) Does the 95% confidence interval support the alternative hypothesis? "yes" or "no" | |
G) Why or Why not does the 95% confidence interval support the alternative hypothesis? |