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 foday results in a mean height of 63.9 inches.
(a) State the appropriate null and atemative hypotheses to assess whether women are taller today
(b) Suppose the P.value for this test is 0.19 . Explain what this value represents.
(c) Write a conclusion for this hypothesis test assuming an $\alpha=0.05$ level of significance.
(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.
A. $H_{6} \mu=63.7$ in. versus $H_{1}: \mu< 63.7$ in
B. $H_{0} \cdot \mu=639$ in. versus $H_{1} ; \mu \neq 639$ in.
C. $H_{0}: \mu=63.9$ in. versus $H_{1} ; \mu> 63.9$ in.
D. $H_{0} ; \mu=63.9$ in versus $H_{1}: \mu< 639$ in.
E. $H_{0} ; \mu=63.7$ in versus $H_{1} ; \mu \neq 63.7$ in
F. $H_{0}: \mu=63.7$ in versus $H_{1} \mu> 637$ in
Answer
Final Answer: \(\boxed{F. H_{0}: \mu=63.7 \text{ in} \text{ versus } H_{1} \mu>63.7 \text{ in}}\)
Step 1 ：The question is asking for the appropriate null and alternative hypotheses to assess whether women are taller today. The null hypothesis is usually a statement of no effect or no difference. In this case, the null hypothesis would be that the mean height of women today is the same as it was several years ago, which is 63.7 inches. The alternative hypothesis is what we would believe if the null hypothesis is proven to be false. In this case, the alternative hypothesis would be that the mean height of women today is greater than it was several years ago.
Step 2 ：Therefore, the correct hypotheses would be: Null hypothesis (\(H_{0}\)): \(\mu=63.7\) in Alternative hypothesis (\(H_{1}\)): \(\mu>63.7\) in
Step 3 ：So, the answer is F. \(H_{0}: \mu=63.7\) in versus \(H_{1} \mu>63.7\) in
Step 4 ：Final Answer: \(\boxed{F. H_{0}: \mu=63.7 \text{ in} \text{ versus } H_{1} \mu>63.7 \text{ in}}\)
