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:

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of glucose per
deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour
fast, the random variable x will have a distribution that is
approximately normal with mean μ = 87 and standard deviation σ =
25. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of
glucose per deciliter (1/10 of a liter) of blood. Suppose that
after a 12-hour fast, the random variable x will have a
distribution that is approximately normal with mean ? = 89
and standard deviation ? = 30. Note: After 50
years of age, both the mean and standard deviation tend to
increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of
glucose per deciliter (1/10 of a liter) of blood. Suppose that
after a 12-hour fast, the random variable x will have a
distribution that is approximately normal with mean ? = 82
and standard deviation ? = 20. Note: After 50
years of age, both the mean and standard deviation tend to
increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of
glucose per deciliter (1/10 of a liter) of blood. Suppose that
after a 12-hour fast, the random variable x will have a
distribution that is approximately normal with mean μ = 83
and standard deviation σ = 21. Note: After 50
years of age, both the mean and standard deviation tend to
increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of
glucose per deciliter (1/10 of a liter) of blood. Suppose that
after a 12-hour fast, the random variable x will have a
distribution that is approximately normal with mean μ = 82
and standard deviation σ = 23. Note: After 50
years of age, both the mean and standard deviation tend to
increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of
glucose per deciliter (1/10 of a liter) of blood. Suppose that
after a 12-hour fast, the random variable x will have a
distribution that is approximately normal with mean μ = 86
and standard deviation σ = 26. Note: After 50
years of age, both the mean and standard deviation tend to
increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of glucose per
deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour
fast, the random variable x will have a distribution that is
approximately normal with mean μ = 80 and standard deviation σ =
27. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of glucose per
deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour
fast, the random variable x will have a distribution that is
approximately normal with mean μ = 89 and standard deviation σ =
23. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of glucose per
deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour
fast, the random variable x will have a distribution that is
approximately normal with mean μ = 82 and standard deviation σ =
26. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of glucose per
deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour
fast, the random variable x will have a distribution that is
approximately normal with mean μ = 89 and standard deviation σ =
29. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

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