Question

A researcher believes that in recent years women have been getting taller. Ten years ago, the average height of young adult women living in his city was 63 inches. The standard deviation is not known. He randomly samples eight young adult women currently residing in the city and measures their heights.

The sample data obtained is: [64, 66, 68, 60, 62, 65, 66, 63]. Use a significance level of alpha=0.05 to test if women are now taller.

Answer 1

Solution: The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Where:

is the sample mean of heights

is the sample standard deviation of heights

is the sample size

  

Now, we need to find the right-tailed critical value at 0.05 significance level for . Using the t distribution table, we have:

Since the t statistic is less than the t critical value, we therefore, fail to reject the null hypothesis at 0.05 significance level and conclude that there is not sufficient evidence to support the claim that in the recent years women have been getting taller.