Question

A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for µd = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypothesis below (versus a two-sided alternative) can be rejected?

A. H0: μd= 0.5B. H0: μd= 1.0C. H0: μd= 1.5D. H0: μd= 2.0

Answer 1

Answer:

Correct option is (A). H₀: $\mu_{d}$ = 0.5

Step-by-step explanation:

The (1 - α)% confidence interval for a population parameter can be used to determine whether to reject a null hypothesis or not.

The decision rule is:

If the (1 - α)% confidence interval for a population parameter consists of the null value of the parameter then the null hypothesis will be accepted or else it will be rejected.

A hypothesis test is performed to determine the difference between the ideal and actual heights of college males.

The 95% confidence interval for the mean difference, $\mu_{d}$ is:

CI = (0.8, 2.2)

The four null hypothesis provided are:

1. H₀: $\mu_{d}$ = 0.5
2. H₀: $\mu_{d}$ = 1.0
3. H₀: $\mu_{d}$ = 1.5
4. H₀: $\mu_{d}$ = 2.0

The 95% confidence interval for the mean difference consists of the value, 1.0, 1.5 and 2.0.

But it does not consist the value 0.5.

So, the null hypothesis that can be rejected is:

H₀: $\mu_{d}$ = 0.5

Thus, the correct option is (A).