Answer:
Step-by-step explanation:
The data in the question is not well arranged. The correct arrangement is:
Before After difference
283 215
299 206
274 187
284 212
248 178
275 212
293 192
277 196
Solution:
a) This is a matched pair design/experiment. This is so because the measurement of cholesterol levels were carried out on the same individuals.
b) Corresponding cholesterol levels before and after treatment form matched pairs.
The data for the test are the differences between the cholesterol levels before and after treatment.
μd = cholesterol level before treatment minus cholesterol level after treatment.
Before After difference
283 215 68
299 206 93
274 187 87
284 212 72
248 178 70
275 212 63
293 192 101
277 196 81
Sample mean, xd
= (68 + 93 + 87 + 72 + 70 + 63 + 101 + 81)/8 = 79.4
xd = 79.4
Standard deviation = √(summation(x - mean)²/n
n = 8
Summation(x - mean)² = (68 - 79.4)^2 + (93 - 79.4)^2 + (87 - 79.4)^2 + (72 - 79.4)^2 + (70 - 79.4)^2 + (63 - 79.4)^2 + (101 - 79.4)^2 + (81 - 79.4)^2 = 1253.88
Standard deviation = √(1253.88/8)
sd = 12.52
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
This is a one tailed test(left tailed test)
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 8 - 1 = 7
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (79.4 - 0)/(12.52/√8)
t = 17.94
We would determine the probability value by using the t test calculator.
p < 0.00001
4) Assume alpha = 0.05
Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, at 5% level of significance, we cannot conclude that the mean cholesterol level after treatment is less than the mean before treatment.
