According to a survey, the mean height for men is 68.9 inches. In a sample of 320 men between the ages of 60 and 69 , the mean height was $\bar { x } = 68.6$ 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 $\sigma = 2.82$ inches, compute the P-value.
A) 0.0287
B) -1.9030
C) 0.0574
D) 0.9713

Question

Quizplus · Accepted Answer

We can use a one-sample t-test to test the hypothesis. The null hypothesis is that the mean height for older men is equal to the mean height for all adult men ($\mu = 68.9$ inches) and the alternative hypothesis is that the mean height for older men is less than the mean height for all adult men ($\mu < 68.9$ inches).

The test statistic is calculated as:

$$t = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} = \frac{68.6 - 68.9}{\frac{2.82}{\sqrt{320}}} = -2.09$$

Using a t-distribution table with 319 degrees of freedom (320-1), we can find the P-value to be approximately 0.0287 for a one-tailed test.

Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that the mean height for older men is less than the mean height for all adult men.

According to a Survey, the Mean Height for Men Is xˉ=68.6\bar { x } = 68.6xˉ=68.6

According to a Survey, the Mean Height for Men Is $\bar { x } = 68.6$