Question

Some of the statements below refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p).

1. The mean number of years Americans work before retiring is 34. (out of the following)

A. H0: p = 34, Ha: p ≠ 34
B. H0: μ = 34, Ha: μ ≠ 34
C. H0: p ≥ 34, Ha: p < 34
D. H0: p ≤ 34, Ha: p > 34
E. H0: μ ≤ 34, Ha: μ > 34
F.H0: μ ≠ 34, Ha: μ = 34
G. H0: μ ≥ 34, Ha: μ < 34
H. H0: p ≠ 34, Ha: p = 34

Answer 1

The correct null hypothesis (H0) is that the mean number of years Americans work before retiring is 34 (μ = 34), and the alternative hypothesis (Ha) is that the mean is not equal to 34 (μ ≠ 34). Therefore, the correct option is B. H0: μ = 34, Ha: μ ≠ 34.

The question is asking to identify the correct null hypothesis (H0) and the alternative hypothesis (Ha) for a statement regarding the average number of years Americans work before retiring. Since the parameter in question is the mean (average), we use the symbol μ (mu) to represent it, not p, which is typically used to represent a proportion.

To set up hypotheses for a two-sided test, we would say that the null hypothesis is that the mean number of years is equal to 34, and the alternative hypothesis is that the mean is not equal to 34. This is expressed as:

H0: μ = 34

Ha: μ ≠ 34

Therefore, the correct answer from the provided options is:

B. H0: μ = 34, Ha: μ ≠ 34