Question

Problem 1.A
A sample of 21 observations was taken. The sample average (20.44) and the sample variance (2.90) were calculated. Take the hypothesis test by the three methods:
Ho µ = 21.5
Ha µ ≠ 21.5
to:

a.Calculating the appropriate limits in terms of Xb for 95% reliability (sample average). (10 pts)

b. Calculate the limits in terms of the appropriate test statistic for 95% reliability and find the corresponding test statistic. (10 pts)

c. Calculate the p-value for this hypothesis test. (10 pts)

Problem 1B
A study is carried out, in which 10 individuals participate, to investigate the effect of physical exercise on plasma cholesterol level. Before exercise, blood samples were taken to determine the cholesterol level of each individual. The participants then underwent an exercise program. At the end of the exercises blood samples were taken again and a second cholesterol level reading was obtained. The results are shown below:

Previous level: 182; 230; 160; 200; 160; 240; 260; 480; 263; 240
Back level: 190; 220; 166; 150; 140; 220; 156; 312; 240; 250

It is wanted to know if the physical exercise has reduced the cholesterol level for a confidence level of 95%. Establish the correct hypotheses and test. (20 pts)

Answer 1

ANSWER::

a) 95% CI for sample average is

( 19.6670, 21.2129)

b) t_cal=-2.8525

c) P-value is 0.0098

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