Question

Question #5. Lecture Week 6, Lectures 1 and 2

Supposedly high-fiber diets reduce serum cholesterol levels. The results of two of these diets (the “Nut” diet and the “Oat” diet) were compared. Thirty-two men with high serum cholesterol were randomly allocated to either receive the Nut diet or the Oat diet for a period of six months. The results are shown in the following table.

	Decrease in Cholesterol Level (mg/dl)
Diet	n	Mean	SD
Nut	16	82	25
Oat	25	70	16

Everyone thinks that the Nut diet is better at reducing cholesterol. So from this data, test the claim at 95% confidence that indeed, the cholesterol level decrease with the Nut diet is greater than that from the Oat diet.

State the Null and Alternative Hypotheses (1)

Since it is clearly a t_test statistic, we will be using to test this claim, one needs first of all to test the claim at 95% confidence that the variance in the data of the two diets (populations) are different from one another.

State the Null and Alternative Hypotheses for this test. (1)

Prepare the PDF and state the Decision Rule (1,1)

Determine the test statistic (2)

What is your decision? (1)

Now back to the original question and based on the decision of part (b), prepare the PDF and state the Decision Rule comparing the means of the two diets. (1,1)

Determine the test statistic (2)

State the decision (1)

State the Interpretation. (1)

Answer 1

Question #5. (13 marks) Lecture Week 6, Lectures 1 and 2

Supposedly high-fiber diets reduce serum cholesterol levels. The results of two of these diets (the “Nut” diet and the “Oat” diet) were compared. Thirty-two men with high serum cholesterol were randomly allocated to either receive the Nut diet or the Oat diet for a period of six months. The results are shown in the following table.

	Decrease in Cholesterol Level (mg/dl)
Diet	n	Mean	SD
Nut	16	82	25
Oat	25	70	16

Everyone thinks that the Nut diet is better at reducing cholesterol. So from this data, test the claim at 95% confidence that indeed, the cholesterol level decrease with the Nut diet is greater than that from the Oat diet.

State the Null and Alternative Hypotheses (1)

Since it is clearly a t_test statistic, we will be using to test this claim, one needs first of all to test the claim at 95% confidence that the variance in the data of the two diets (populations) are different from one another.

State the Null and Alternative Hypotheses for this test. (1)

Prepare the PDF and state the Decision Rule (1,1)

Two tailed test

F test is used.

Table value of F(15,24) at 0.05 level=2.4374

If Calculated F > 2.4374, we reject the null hypothesis.

Determine the test statistic (2)

=2.4414

What is your decision? (1)

Calculated F = 2.4414 > 2.4374 the table value

The null hypothesis is rejected.

Now back to the original question and based on the decision of part (b), prepare the PDF and state the Decision Rule comparing the means of the two diets. (1,1)

Upper tail test

Separate-Variances t Test for the Difference Between Two Means used

Determine the test statistic (2)

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	16
Sample Mean	82
Sample Standard Deviation	25.0000
Population 2 Sample
Sample Size	25
Sample Mean	70
Sample Standard Deviation	16.0000
Intermediate Calculations
Numerator of Degrees of Freedom	2430.7365
Denominator of Degrees of Freedom	106.0943
Total Degrees of Freedom	22.9111
Degrees of Freedom	22
Standard Error	7.0216
Difference in Sample Means	12.0000
Separate-Variance t Test Statistic	1.7090
Upper-Tail Test
Upper Critical Value	1.7171
p-Value	0.0508
Do not reject the null hypothesis

State the decision (1)

Calculated t=1.709 < 1.7191 the critical value at 0.05 level.

Ho is not rejected.

State the Interpretation. (1)

There is no evidence to conclude that the cholesterol level decrease with the Nut diet is greater than that from the Oat diet.