Question

Low-density lipoprotein (LDL) is an important part of the blood cholesterol test. The mean LDL for people 65 and older is 130 with a standard deviation of 12. The mean LDL for people under 40 is 100 with a standard deviation of 12. A health center had a free blood cholesterol test for all people in the community. The blood test results for the people under 40 and 65 an over are given in the attached excel file called "Cholesterol Data-2" What is the probability that the mean LDL of 8 people who are 65 or over would exceed the mean LDL of 8 people who are under 40 by the difference in these two samples of more? (give your answer to at least 3 decimal places). Hint: First you have to find the mean and the standard error of the mean of the sampling distribution of the difference between means. Then you have to find the means of both samples. Next you find the difference between the 2 sample means. Finally you use a normal calculator tool

LDL(mg/dl)
65 and over	Under 40
130	120
143	90
114	64
110	77
123	102
110	83
134	127
124	105

Answer 1

Here we have

Let X shows the LDL for the 65 and over group and Y shows the LDL for the under 40 group.

The mean of the sampling distribution of the difference between means is

and the standard error of the difference between means is

Following table shows the sample totals:

	65 and over,X	Under 40, Y
	130	120
	143	90
	114	64
	110	77
	123	102
	110	83
	134	127
	124	105
Total	988	768

Sample size

Mean:

The z-score for is

The probability that the mean LDL of 8 people who are 65 or over would exceed the mean LDL of 8 people who are under 40 by the difference in these two samples of more is