Question

Refer to the accompanying data​ table, which shows the amounts of nicotine​ (mg per​ cigarette) in​ king-size cigarettes,​ 100-mm menthol​ cigarettes, and​ 100-mm nonmenthol cigarettes. The​ king-size cigarettes are​ nonfiltered, while the​ 100-mm menthol cigarettes and the​ 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the​ king-size cigarettes are not​ filtered, do the filters appear to make a​ difference?

King-Size   100-mm_Menthol   Filtered_100-mm_Nonmenthol
1.4   1.2   0.7
1.1   0.9   1.0
1.0   1.2   0.4
1.1   0.9   1.1
1.4   1.2   1.1
1.2   1.3   0.7
1.3   0.9   1.0
1.0   1.1   1.2
1.2   0.9   0.8
1.2   0.8   0.9

1. Determine the null and alternative hypotheses.

2. Find the F statistic.

3. Find the P value.

4. What is the conclusion for this hypothesis test?

A. Reject H 0. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

B. Fail to reject H 0. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

C. Reject H 0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

D. Fail to reject H 0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine

5. Do the filters appear to make a difference?

A. ​No, the filters do not appear to make a difference because there is sufficient evidence to warrant rejection of the claim.

B. No, the filters do not appear to make a difference because there is insufficient evidence to warrant rejection of the claim.

C. The results are inconclusive because the​ king-size cigarettes are a different size than the filtered cigarettes.

D. Given that the king dash size cigarettes have the largest mean comma it appears that the filters do make a difference left parenthesis although this conclusion is not justified by the results from analysis of variance right parenthesis .

Answer 1

From the given data the primary statistics are as below

	King	Menthol	Non Menthol
Total	11.9	10.4	8.9
n	10	10	10
Mean	1.190	1.040	0.89
SS	1.6051	1.3656	1.3211
Variance	0.1783	0.1517	0.147
SD	0.4223	0.3895	0.3831

(1) The Hypothesis:

H0: There is no difference between the mean amount of nicotine from the three categories of cigarettes..

Ha: There is a significant difference in the means of amount of nicotine between at least two of the categories.

________________________________________________________________________________

(2) The Test Statistic:

.The ANOVA table is as below. The calculations are provided after the test,

Source	SS	DF	Mean Square	F	Fcv	p
Between	45.00	2.00	22.50	141.51	3.3541	0.0000
Within/Error	4.29	27.00	0.16
Total	49.29	29.00

F observed = 141.51

(3) The p value is calculated for F = 141.51 for df1 = 2 and df2 = 27; p value = 0.000

(4) Conclusion: Option C: Reject H0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same amount of nicotine.

(5) Option D

(Option A is wrong as we have rejected the claim it means that the mean amount of nicotine is different. Option B is wrong as we do have sufficient evidence and not insufficient evidence. Option C says the evidence is inconclusive because the king sized cigarette length is different

In Option D, the last statement says that ANOVA does not justify the conclusion that filters reduce the nicotine content. This is correct as we have because we have rejected the claim that the means are equal but it could mean that there could be a difference between menthol and non menthol cigarettes too, so the results of ANOVA dont completely justify the fact that although the mean nicotine content in king sized is more than the other 2, the ANOVA result does not justify the fact that it could be because of being a non filter cigarette)