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. ​

(a) State the appropriate null and alternative hypotheses to assess whether women are taller today. ​

(b) Suppose the​ P-value for this test is 0.11. Explain what this value represents. ​

(c) Write a conclusion for this hypothesis test assuming an alpha=0.10 level of significance.

Answer 1

a ) Hypothesis :

b )

There is a .11 probability of obtaining a sample mean height of 64.2 inches or TALLER from a population whose mean height is 63.7 inches.

c )

Decision about null hypothesis :

Rule : Reject null hypothesis if p-value is less than significance level

Here, significance level = 0.10

It is observed that p-value ( 0.11 ) is greater than = 0.10

So , Do not reject the null hypothesis.

Conclusion :

There is not sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today.