Question

Bus. 8.7 A cigarette manufacturer has advertised that it has developed a new brand of cigarette, LowTar, that has a lower average tar content than the major brands. To evaluate this claim, a con- sumer testing agency randomly selected 100 cigarettes from each of the four leading brands of cigarettes and 100 from the new brand. The tar content (milligrams) of the cigarettes gave the fol lowing results: Brand lni LowTar 9.64.291100 .478 10.22 100 10.77 372 100 11.57 352 100 13.59 49 100 A boxplot of the data used to produce the table are given here 15 Boxplots of tar content by brand for Exercise 8.7 (means are indicated by solid circles) 13 10 LowTar Brand a. Based on the information contained in the boxplot, does the LowTar brand appear to have a lower average tar content than the other brands? b. Using the computer output shown here, is there a significant (α-01) difference in the average tar content of the five brands of cigarettes? C. What is the p-value of the test statistic in (b)? d. What are the practical consequences of making a Type I error with respect to your test in (b)?

Answer 1

here null hypothesis H0: all brands have same tar content

alternate hypothesis Ha: atleast one brands has different from others

(a) yes, low Tar brand hav a lower average content than the other brands

(b) yes, p-value of between groups is less than the alpha=0.01, so we reject H0 and we conclude that there is significant difference in the average tar content of the five brands of cigarettes

(c) here p-value=0.000

(d) Type I error is reject H0 when H0 is true, means we are rejecting that all the brands have the same Tar content actually atleast one brands is different from others

following information has been generated using ms-excel

					within SS		between SS
Group	nj	mean(xj-)	s2	nj*xj-	(n-1)s2	(xj--x-)	nj(xj--x-)2
1	100	9.64	0.084681	964	8.383419	-1.518	230.4324
2	100	10.22	0.228484	1022	22.619916	-0.938	87.9844
3	100	10.77	0.138384	1077	13.700016	-0.388	15.0544
4	100	11.57	0.123904	1157	12.266496	0.412	16.9744
5	100	13.59	0.219961	1359	21.776139	2.432	591.4624
sum	500	55.79	0.795414	5579	78.745986	3.55E-15	941.908
grand mean(x-)	11.158
		ANOVA
SOURCE	DF	SS	MS	F	CRITICAL F(0.05)	p-value
BETWEEN	4	941.91	235.477	1480.22	2.39	9.5E-274
WITHIN(ERROR)	495	78.75	0.159083
TOTAL	499	1020.65