Question

For a two-tailed hypothesis test at the significance level alpha, the null hypothesis H0: μ = μ0 will be rejected in favor of the alternative hypothesis Ha: μ≠ μ0 if and only if μ0 lies outside the (1 - α) level confidence interval for μ. Illustrate the preceding relationship by obtaining the appropriate one-mean z-interval for the data below.

Suppose the mean height of women age 20 years or older in a certain country is 62.8 inches. One hundred randomly selected women in a certain city had a mean height of 61.6 inches. At the 10% significance level, the data provide sufficient evidence to conclude that the mean height of women in the city differs from the national mean. Assume that the population standard deviation of the heights of women in the city is 3.7 inches.

The confidence interval is ( ), ( ) (Round to two decimal places as needed.)

Answer 1

for test statistic falls in rejection region ; we reject null hypothesis

we have sufficient evidence at 0.10 level to conclude that mean height of women in the city differs from the national mean.

b)

for 95 % CI value of z=				1.960
margin of error E=z*std error                            =				0.725
lower confidence bound=sample mean-margin of error=				60.87
Upper confidence bound=sample mean +margin of error=				62.33

confidence interval is 60.87 to 62.33