Question

A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

Clothes Food Toys

43	30	52
24	38	58
42	46	43
35	54	49
28	47	63
31	42	53
17	34	48
31	43	58
20	57	47
	47	51
	44	51
	54

a. Complete the ANOVA table using a .05 significance level (Round the SS and MS values to 1 decimal place and F value to 2 decimal places. Leave no cells blank — be certain to enter "0" wherever required. Round the df values to nearest whole number.)

b. Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)

c. Is there a difference in the mean attention span of the children for the various commercials?

	The hypothesis of identical means can definitely be (Rejected or Not Rejected) . There is (A difference, No difference) in the mean attention span.

d.

Are there significant differences between pairs of means?

	Clothes have a mean attention span of at least ten minutes (Above or Below) the other groups.

Answer 1

One-way ANOVA: cloths, food, toys

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 3 cloths, food, toys

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 2437 1218.52 20.81 0.000
Error 29 1698 58.57
Total 31 4136

Model Summary

S R-sq R-sq(adj) R-sq(pred)
7.65296 58.93% 56.10% 49.78%

Means

Factor N Mean StDev 95% CI
cloths 9 30.11 9.01 (24.89, 35.33)
food 12 44.67 8.11 (40.15, 49.19)
toys 11 52.09 5.72 (47.37, 56.81)

Pooled StDev = 7.65296

a)

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 2437 1218.52 20.81 0.000
Error 29 1698 58.57

Total 31 413

b)

Factor N Mean StDev

cloths 9 30.11 9.01
food 12 44.67 8.11
toys 11 52.09 5.72

c)

p value =0 < alpha

we reject null hypothesis,there is sufficient evidence to support that atleast two of the mean is differ from the other

d)all differences are significant