Question

A researcher would like to find out whether a man's nickname affects his cholesterol reading (though it is not clear why she believes it should). She records the cholesterol readings of 10 men nicknamed Sam, 10 men nicknamed Lou and 10 men nicknamed Mac; her data appears in the table. She wants to know whether there is a difference in cholesterol levels in men with these 3 nicknames. Present all appropriate statistical test need to determine if a difference exists. Provide all your proofs. The data have been tested and are considered normally distributed.

Sam	Lou	Mac
364	260	156
245	204	438
284	221	272
172	285	345
198	308	198
239	262	137
259	196	166
188	299	236
256	316	168
263	216	269

Answer 1

ANSWER:

Given that,

Since we are testing the equality of more than 2 means, we use the ANOVA F- test.

The table below gives the data which has been calculated from the given figures

	Sam	Lou	Mac
Mean	246.8	256.7	238.5
Variance	3012.622	2018.9	9130.7222
SD	54.887	44.932	95.555

The Hypothesis:

H0: There is no difference between the means of the cholesterol level for the men with these 3 names.

Ha: There is a difference between the mean cholesterol level for the men with these names.

The ANOVA table is as below. the p value is calculated for F = 0.176 for df1 (column-1) = 3-1 = 2 and df2 (total observations - # of columns) = 30 - 3 = 27

The F-critical is calculated at = 0.05(default) for df1 = 2 and df2 = 27

Source	Sum of sq	DF	Mean Square	F	Fcv	p
Between	1660.47	2	830.23	0.176	3.354	0.8396
Within	127456.60	27	4720.61
Total	129117.07	29

The F- stat = 0.176

The Decision Rule:

If F-test is > F critical, Then Reject H0.

Also if p-value is < , Then reject H0.

The Decision:

Since F-test (0.176) is < F critical (3.354), We Fail to Reject H0.

Also since p-value (0.8396) is > (0.05), We Fail to reject H0.

The Conclusion:

There is insufficient evidence at the 95% level of significance to conclude that there is a difference between the mean cholesterol level of the mean with these names.