Question

Obesity is a topic of ongoing health concern. A random sample of 25 adult males were examined and found to be an average of 18 pounds overweight, with a standard deviation of 10 pounds. These results will be used to address the following statistical question: Do these results provide evidence that, on average, adult males are overweight more than the 15 pounds reported by a television documentary?

1. Using appropriate notation, state the null hypothesis and the alternative hypothesis.

2. Compute the value of the test statistic.

3.  Using a significance level of a = 0.05, identify the rejection region.

4. Make a decision and explain what it means in terms of obesity of adult males. Fully justify your decision.

5. Construct a 90% confidence interval for the mean amount by which adult males are overweight. Explain what this confidence interval means in terms of obesity of adult males.

6. Determine the sample size necessary in order to estimate the mean to within 0.5 pounds with 80% confidence.

Answer 1

3)At 5% significance level, we can reject H0 only if t*>t(0.95,24dof)=1.71

Hence rejection region->t>1.71

4)As t*<1.71, we fail to reject H0. It means that there is not enough evidence to say that the adult males are overweight by more than 15pounds

The interval means that if we take infinitely many samples of size 25, we would 90% of time find the mean overweight to be between 14.58 and 21.42