Suppose that the heights of 12-year-old boys are known to be normally distributed with a mean of 59.1 in. and a standard deviation of 2.5 in. A researcher suspects that children from high-income families have better access to nutritious food and are able to grow taller than children from lower-income families. To test this, he selects a random sample of 95 12-year-old boys from high-income families and finds that their mean height is 59.3 in. He plans to use this information to conduct a one-sample z-test.

What is the claim that he is testing?

A. The mean height of 12-year-old boys from high-income families is 59.1 in.
B. The mean height of all 12-year-old boys is 59.1 in.
C. The mean height of the 95 12-year-old boys in the sample is greater than 59.1 in.
D. The mean height of 12-year-old boys from high-income families is 59.3 in.
E. The mean height of 12-year-old boys from high-income families is greater than 59.1 in.

The researcher's claim being tested in the one-sample z-test is that the mean height of 12-year-old boys from high-income families is greater than 59.1 inches.

Explanation:

The claim that the researcher is testing with a one-sample z-test is whether the mean height of 12-year-old boys from high-income families is different from the known mean height of all 12-year-old boys. Given the information, the correct claim for the hypothesis being tested would be: e. The mean height of 12-year-old boys from high-income families is greater than 59.1 in.

This is because the researcher is comparing the sample mean of boys from high-income families to the overall population mean (59.1 inches) to see if the sample mean is significantly higher, which might suggest that the high-income environment has an effect on the children's growth.