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 64.9 inches.
(a) State the appropriate null and altemative hypotheses to assess whether women are taller today.
(b) Suppose the P-value for this test is 0.08 . Explain what this value represents.
(c) Write a conclusion for this hypothesis test assuming an $\alpha=0.10$ level of significance.
t. $H_{0} \mu=b 3.1$ in versus $H_{1}, \mu> 03.1$ in.
(b) Suppose the P-value for this test is 0.08 . Explain what this value represents.
A. There is a 0.08 probability of obtaining a sample mean height of exactly 64.9 inches from a population whose mean height is 63.7 inches.
B. There is a 0.08 probability of obtaining a sample mean height of 64.9 inches or shorter from a population whose mean height is 63.7 inches.
C. There is a 0.08 probability of obtaining a sample mean height of 64.9 inches or taller from a population whose mean height is 63.7 inches.
D. There is a 0.08 probability of obtaining a sample mean height of 63.7 inches or taller from a population whose mean height is 64.9 inches.
Answer
Final Answer: \(\boxed{H_{0}: \mu = 63.7\) inches, \(H_{1}: \mu > 63.7\) inches}
Step 1 ：State the appropriate null and alternative hypotheses to assess whether women are taller today. The null hypothesis is that the mean height of women today is equal to the mean height of women several years ago, which is 63.7 inches. The alternative hypothesis is that the mean height of women today is greater than the mean height of women several years ago.
Step 2 ：Null Hypothesis, \(H_{0}: \mu = 63.7\) inches
Step 3 ：Alternative Hypothesis, \(H_{1}: \mu > 63.7\) inches
Step 4 ：Where \(\mu\) represents the mean height of women today.
Step 5 ：The P-value for this test is 0.08. This value represents the probability of obtaining a sample mean height of 64.9 inches or taller from a population whose mean height is 63.7 inches.
Step 6 ：Write a conclusion for this hypothesis test assuming an \(\alpha=0.10\) level of significance. Since the P-value is less than the level of significance, we reject the null hypothesis. There is sufficient evidence to conclude that the mean height of women today is greater than the mean height of women several years ago.
Step 7 ：Final Answer: \(\boxed{H_{0}: \mu = 63.7\) inches, \(H_{1}: \mu > 63.7\) inches}
