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? Click the icon to view the data table of the nicotine amounts. Find the F test statistic F = 2.8803 (Round to four decimal places as needed.) Find the P-value using the F test statistic. P-value = 0.0735 (Round to four decimal places as needed.) What is the conclusion for this hypothesis test? O A. Reject Hn. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine. Question is complete. Tap on the red Indicators to see incorrect answers.

Answer 1

count, ni =	10	10	10
mean , x̅ i =	1.190	1.04	0.95
std. dev., si =	0.2	0.2	0.2
sample variances, si^2 =	0.061	0.036	0.056
total sum	11.9	10.4	9.5				31.8	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	1.06
( x̅ - x̅̅ )²	0.017	0.000	0.012
							TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	0.169	0.004	0.121				0.294
SS(within ) = SSW = Σ(n-1)s² =	0.549	0.324	0.505				1.3780

no. of treatment , k =   3      
df between = k-1 =    2      
N = Σn =   30      
df within = N-k =   27      
          
mean square between groups , MSB = SSB/k-1 =    0.294/2=   0.1470  
mean square within groups , MSW = SSW/N-k =    1.378/27=   0.0510  
          
F-stat = MSB/MSW =    0.147/0.051=   2.8803
          
P value =   0.0735      

	SS	df	MS	F	p-value	F-critical
Between:	0.3	2	0.1	2.9	0.073	3.354
Within:	1.4	27	0.1
Total:	1.7	29
					α =	0.05
					Decision:	p-value>α , do not reject null hypothesis

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