Question

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

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)

Answer 1

mean LDL for people 65 and older = M1=  130

standard deviation LDL for people 65 and older = S1= 12

The mean LDL for people under 40 =M2=100

standard deviation LDL for people under 40 =S2=12

N1 = N2 =8

Mean difference = 130-100 =30

standard error of the difference between means =

=√ S12/N1  + S2/N2

PUTTING VALUES WE GET = 6

	65 and over	40 and under
	130	120
	143	90
	114	64
	110	77
	123	102
	110	83
	134	127
	124	105
	988	768
Mean	123.5	96

Difference = 123.5 - 96 = 27.5

µ =    30              
σ =    6              
                  
P ( X ≥   27.50   ) = P( (X-µ)/σ ≥ (27.5-30) / 6)          
= P(Z ≥   -0.42 ) = P( Z <   0.42 ) =    0.663

Please revert back in case of any doubt.

Please upvote. Thanks in advance.