### Hypothesis Testing on the Average Height of WomenSeveral years ago, the mean height of women aged 20 years 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. This analysis aims to assess whether women's average height today is significantly taller.#### (a) State the Null and Alternative HypothesesTo evaluate whether women are taller today, we compare:- **Option D:** \( H_0: \mu = 63.7 \) in. versus \( H_1: \mu > 63.7 \) in.This setup tests if the current average height exceeds the previously recorded 63.7 inches.#### (b) P-Value InterpretationThe P-value for this test is 0.18. This value represents:- **Option A:** There is a 0.18 probability of obtaining a sample mean height of 64.9 inches or taller from a population whose mean height is 63.7 inches.The P-value measures the likelihood of observing such a result if the null hypothesis were true.#### (c) Conclusion with α = 0.05Based on a significance level of 0.05, we conclude:- **Option C:** 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 today.The P-value of 0.18 exceeds the 0.05 significance threshold, suggesting that the observed increase may be due to random variation rather than a true increase in average height.

The question is about hypothesis testing.Given :Population mean height of women 20 years of age or…

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 alternative hypotheses to assess whether women are taller today (b) Suppose the P-value for this test is 0.18. Explain what this value represents. k (c) Write a conclusion for this hypothesis test assuming an a= 0.05 level of significance. (a) State the appropriate null and alternative hypotheses to assess whether women are taller today. III OA. Ho H=63.7 in. versus H₁ µ#63.7 in OC. Ho p=63.7 in. versus H, u>63.7 in. OE. Ho H=64.9 in. versus H₁ μ#64.9 in (b) Suppose the P-value for this test is 0.18. Explain what this value represents. OA. There is a 0.18 probability of obtaining a sample mean height of 64.9 inches or taller from a population whose mean height is 63.7 inches OB. There is a 0.18 probability of obtaining a sample mean height of 64.9 inches or shorter from a population whose mean height is 63.7 inches. OC. There is a 0.18 probability of obtaining a sample mean height of exactly 64.9 inches from a population whose mean height is 63.7 inches. O D. There is a 0.18 probability of obtaining a sample mean height of 63.7 inches or taller from a population whose mean height is 64.9 inches. (c) Write a conclusion for this hypothesis test assuming an a=0.05 level of significance. OB. Ho H=64.9 in. versus H₁ u<64.9 in. O D. Ho H=64.9 in versus H₁ H> 64.9 in. OF. Ho H=63.7 in. versus H₁ μ< 63.7 in. O A. 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. OB. 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. OC. 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. OD. 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.