According to a survey, the mean height for men is 68.6 inches. In a sample of 320 men between the ages of 60 and 69 , the mean height was $\bar { x } = 68.5$ inches. Public health officials want to determine whether the mean height $\mu$ for older men is less than the mean height of all adult men. Assuming the population standard deviation to be $\sigma = 2.85$ inches, compute the value of the test statistic.
A) 0.74
B) 429.95
C) -0.63
D) 0.63

Question

Quizplus · Accepted Answer

We want to test whether the population mean height for older men is less than the mean height of all adult men. The null hypothesis is:

H0: μ ≥ 68.6
The alternative hypothesis is:

Ha: μ < 68.6

We will use a one-sample t-test with a significance level of 0.05.

The formula for the t-statistic is:

t = (x̄ - μ) / (σ / √n)

where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (68.5 - 68.6) / (2.85 / √320) = -0.63

The test statistic is -0.63.

Since this is a one-tailed test with a significance level of 0.05, we compare the test statistic to the critical value of t with 319 degrees of freedom and a significance level of 0.05. The critical value is -1.645.

Since -0.63 > -1.645, we fail to reject the null hypothesis. There is not enough evidence to suggest that the mean height for older men is less than the mean height of all adult men.

According to a Survey, the Mean Height for Men Is xˉ=68.5\bar { x } = 68.5xˉ=68.5

According to a Survey, the Mean Height for Men Is $\bar { x } = 68.5$