Question

Several years​ ago, the mean height of women 20 years of age or older was 63.7 inches. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 64.7 inches. ​

(a) State the appropriate null and alternative hypotheses to assess whether women are taller today. ​

(b) Suppose the​ P-value for this test is 0.12 . Explain what this value represents.

​(c) Write a conclusion for this hypothesis test assuming an alpha equals0.05 level of significance.

Answer 1

Solution:

(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.

The null and alternative hypotheses for the given hypothesis test are given as below:

Null hypothesis: H₀: The mean height of women 20 years of age or older is 63.7 inches.

Alternative hypothesis: H_a: The mean height of women 20 years of age or older is greater than 63.7 inches.

H₀: µ = 63.7 versus H_a: µ > 63.7

This is an upper or right tailed test.

(b) Suppose the​ P-value for this test is 0.12 . Explain what this value represents.

The P-value for this test is given as 0.12, which represent that the minimum probability or significance level at which we do not reject the null hypothesis that the mean height of women 20 years of age or older is 63.7 inches.

​(c) Write a conclusion for this hypothesis test assuming an alpha equals0.05 level of significance.

We are given

P-value = 0.12

α = 0.05

P-value > α

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that the mean height of women 20 years of age or older is greater than 63.7 inches.