Question

A nutrition expert claims that the average American is overweight. To test his claim, a random sample of 22 Americans was selected, and the difference between each person's actual weight and idea weight was calculated. For this data, we have x¯=18.2x¯=18.2 and s=29.4s=29.4. Is there sufficient evidence to conclude that the expert's claim is true? Carry out a hypothesis test at a 4% significance level.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a)(−∞,a) is expressed (-infty, a), an answer of the form (b,∞)(b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞)(−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Do Not Reject H1H1.
B. Reject H1H1.
C. Reject H0H0.
D. Do Not Reject H0H0.

Answer 1

A)

This is a paired t-test.

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

B)

Since this is a right-tailed test, so the rejection region is given by:

C)

Since this is a right-tailed test, so the p-value is given by:

D)

Since p-value is less than 0.04, so we have sufficient evidence to reject the null hypothesis H0.

Hence option C.

There is sufficient evidence to say that the claim is true.