Question

Are older men shorter than younger men? According to a national report, the mean height for U.S. men is 69.4 inches. In a sample of 119 men between the ages between of 60 and 69 and, the mean height was 69.3 inches. Public health officials want to determine whether the mean height for older men is less than the mean height of all adult men. Assume the population standard deviation to be 2.58. Use the a=0.05 level of significance and the-value method with the table.

Answer 1

Solution:

Given ,

= 69.4

claim : < 69.4

n = 119

= 69.3

= 2.58

Use = 0.05

a) Hypothesis are

H0 : = 69.4 (null hypo.)

H1 :   < 69.4

b)The test statistic z is given by

z =

= (69.3 - 69.4) / (2.58/119)

= -0.42

Now , observe that ,there is < sign in H1. So , the test is left tailed.

For left tailed test :

p value = P(Z < z)

= P(Z < -0.42)

= 0.3372 (use z table)

Use the a=0.05 level of significance

p value is greater than 0.05

So , fail to reject the null hypothesis and conclude that the  the mean height for older men is NOT significantly less than the mean height of all adult men.