Question

A group of adults with elevated cholesterol levels participated in a diet and exercise program to...

A group of adults with elevated cholesterol levels participated in a diet and exercise program to determine the effect of this program on their cholesterol. The resulting data follows:

 Subject Before After 1 259 244 2 260 250 3 272 246 4 260 235 5 281 273 6 254 245

Test the hypothesis that the diet and exercise program lowered the subject's total chloresterol by at least
15 points. alpha = .05.
a. Find the mean of the differences.
b. Find the standard deviation of the differences.
c. Find the lower confidence limit of the differences.
d. Find the upper confidence limit of the differences.
e. According to the confidence interval, the null hypotesis that the difference is equal to 20 cannot be rejected.

TRUE

FALSE

 Subject Before After Difference 1 259 244 15 2 260 250 10 3 272 246 26 4 260 235 25 5 281 273 8 6 254 245 9 Total 93

Sample size = n = 6

a) Sample mean of difference =    = 15.5

b) Standard deviation of difference = = 8.1179

c) We have to construct 95% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 5 - 1 = 4

Level of significance = 0.05

tc = 2.571 ( Using t table)

So confidence interval is ( 15.5 - 8.5192 , 15.5 + 8.5192) = > ( 6.9808 , 24.0192)

c) Lower confidence limit = 6.9808

d) Upper confidence limit = 24.0192

e) TRUE because 20 is lies into interval.

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