Question

5. The head football coach is concerned about high cholesterol level of the assistant coaches. In an
attempt to improve the situation a sample of seven coaches is selected to take part in a special program
in which each coach is given a special diet by the school trainer. After six months each coach’s
cholesterol level is checked again. At the .01 level of significance, can we conclude that the program led
to a change in the cholesterol levels?
Coach Before After
1.            225.   210
2.            230.   225
3.            290.   215
4.             242. 215
5.             300. 240
6.             250. 235
7.            215.   190.                                              1. State the hypotheses:
2. Determine the critical values and diagram.
3. Identify the test statistic:
4. What is the decision rule?
5. Calculate the test statistic:
6. Conclusion and justification
Type of error:
7. p-value:

Answer 1

Solution:

Paired t-test

1. State the hypotheses:

Null hypothesis: H₀: The program doesn’t lead to a change in the cholesterol levels.

Alternative hypothesis: H_a: The program led to a change in the cholesterol levels.

H₀: µ_D = 0 versus H_a: µ_D ≠ 0

2. Determine the critical values and diagram.

We are given

n = 7

df = n – 1 = 6

α = 0.01

so, critical values = -3.7074 and 3.7074

(by using t-table or excel)

3. Identify the test statistic:

Test statistic = t = (Dbar - µ_D) / [S_D/sqrt(n)]

4. What is the decision rule?

Reject H₀ when test statistic |t|> 3.7074

5. Calculate the test statistic:

From given data, we have

Dbar = -31.7143

S_D = 25.8632

n = 7

Test statistic = t = (-31.7143 – 0)/[ 25.8632/sqrt(7)]

Test statistic = t = -3.2443

6. Conclusion and justification

|t| = 3.2443 < critical value = 3.7074

So, we do not reject the null hypothesis H₀

There is insufficient evidence to conclude that the program led to a change in the cholesterol levels.

Type of error: Type II error

7. p-value:

P-value = 0.0176

(By using t-table or excel)