According to the NHSR, the mean height for US men in 69.4 inches. In a sample of 300 men between 60 and 69, the mean height was 69 inches. Public health officials want to determine whether the mean height for older men is different than mean height of all adults. Assume the population standard deviation is 2.84 inches. Perform a hypothesis test at the level of significance α=0.01. State null hypothesis

Question

H0: μ
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State alternative hypothesis

H1: μ
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Answer 1

To state the null and alternative hypotheses for the given scenario, we need to define what we are testing.

Given that:

• The population mean height for US men, as per the NHSR, is 69.4 inches.
• The sample mean height for men aged between 60 and 69 is 69 inches.
• The population standard deviation (σ) is 2.84 inches.
• The sample size (n) is 300.
• The significance level (α) is 0.01.

We can state the hypotheses as follows:

Null Hypothesis (H0): The mean height of older men (aged 60-69) is equal to the mean height of all US adult men.

\[ H_0: \mu = 69.4 \]

Alternative Hypothesis (H1): The mean height of older men (aged 60-69) is different from the mean height of all US adult men.

\[ H_1: \mu \neq 69.4 \]

This sets up a two-tailed test, as we are checking for any difference (not specifying whether it is greater or smaller) between the two means.