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 64.1 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 0.13. explain what this value represents
(c) write a conclusion for this hypothesis test assuming an \\( \alpha = 0.05 \\) level of significance
b. there is a 0.13 probability of obtaining a sample mean height of 64.1 inches or shorter from a population whose mean height is 63.7 inches
c. there is a 0.13 probability of obtaining a sample mean height of 63.7 inches or taller from a population whose mean height is 64.1 inches
d. there is a 0.13 probability of obtaining a sample mean height of exactly 64.1 inches from a population whose mean height is 63.7 inches
(c) write a conclusion for this hypothesis test assuming an \\( \alpha = 0.05 \\) level of significance
a. do not reject the null hypothesis. there is not sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today
b. reject the null hypothesis. there is sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today.
c. do not reject the null hypothesis. there is sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today
d. reject the null hypothesis. there is not sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today

Explanation:

• For hypothesis testing, the decision rule is: if \(P - value\geq\alpha\), we do not reject the null hypothesis. Here, \(\alpha = 0.05\) and \(P - value=0.13\). Since \(0.13\geq0.05\), we do not reject the null hypothesis.
• The null hypothesis \(H_0:\mu = 63.7\) (where \(\mu\) is the population mean height) and the alternative hypothesis \(H_1:\mu> 63.7\) (testing if women are taller today). Not rejecting \(H_0\) means there is not enough evidence to support \(H_1\).

Answer:

A. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today.