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 64.2 inches
1. State the appropriate null and alternative hypotheses to assess whether women are taller today.

A) H0: u = 64.2 in. versus H1: u not equal to 64.2 in.

B) H0: u = 63.7 in. versus H1: u not equal to 63.7 in.

C) H0: u = 63.7 in. versus H1: u > 63.7 in.

D) H0: u = 63.7 in. versus H1: u < 63.7 in.

E) H0: u = 64.2 in. versus H1: u > 64.2 in.

F) H0: u = 64.2 in. versus H1: u < 64.2 in.


2. Suppose the P-value for this test is 0.18. Explain what this value represents.

A) 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 64.2 inches.

B) There is a 0.18 probability of obtaining a sample mean height of exactly 64.2 inches from a population whose mean height is 63.7 inches.

C) There is a 0.18 probability of obtaining a sample mean height of 64.2 inches or taller from a population whose mean height is 63.7 inches.

D) There is a 0.18 probability of obtaining a sample mean height of 64.2 inches or shorter from a population whose mean height is 63.7 inches.


3. Write a conclusion for this hypothesis test assuming an a = 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) 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.

D) Do not reject the null hypothesis. There is sufficient evenidence that the mean height of women 20 years of age or older is greater today.

Answer 1

Answer:

1. C) H0: u = 63.7 in. versus H1: u > 63.7 in.

2. B). There is a 0.18 probability of obtaining a sample mean height of exactly 64.2 inches from a population whose mean height is 63.7 inches.

3. 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.

Step-by-step explanation:

1. C) H0: u = 63.7 in. versus H1: u > 63.7 in.

the null hypothesis state that over the years the mean height is 63.7in. the alternative hypothesis will be if the mean height is greater than 63.7

2. z = (variate - mean)/ (standard deviation/$\sqrt{N}$

Z = (64.2 - 63.7)/ (20/roots 45) =0.17

meaning there is

B. There is a 0.18 probability of obtaining a sample mean height of exactly 64.2 inches from a population whose mean height is 63.7 inches.

3. if the level of significance is 0.05 or between  0.05 and 0.01, i.e. the confidence level is 95% or  between 95% and 99%, the results are considered  to be probably significant, i.e. the results  are probably correct,

therefore, the alternative hypothesis is correct

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.