Question

The level of blood glucose and diabetes in adults are related. Let X1 be a random variable measured in milligrams of glucose per deciliter (one-tenth of a liter) of blood for females in the U.S. Let X2 be a random variable measured in milligrams of glucose per deciliter of blood for males. After a 12-hour fast, the random variables X1 and X2 are normally distributed, with the following population parameters:

Females: Mean = 85 and standard deviation = 25

Males: Mean = 82 and standard deviation = 22

A simple random sample of 26 adult females is taken and a simple random sample of 33 adult males is taken.

A) Is the sampling distribution of the difference between the mean blood glucose levels of females and males normally distributed? Why or why not?

B) Calculate the mean of the sampling distribution of the difference between the mean blood glucose levels of females and males.

C) Calculate the standard deviation of the sampling distribution of the difference between the mean blood glucose levels of females and males.

Answer 1

(A)
The sampling distribution of the difference between the the blood glucose levels of females and males not normally distributed because it is given that X1and X2 are normally distributed. Population standard deviations are given.

(B)

Mean of sampling distribution of the difference between the the blood glucose levels of females and males = 85 - 82 = 3.

(C) Standard deviation of the sampling distribution of the difference between the the blood glucose levels of females and males is given as follows: