For a two-tailed hypothesis test at the significance level , the null hypothesis H0 : =

For a two-tailed hypothesis test at the significance level α, the null hypothesis H0 : μ = μ0 will be rejected in favor of the alternative hypothesis H0 : 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 62.3 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 3.6 inches.