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}