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.

Item	Length
Clothes	28
Clothes	16
Clothes	51
Clothes	35
Clothes	28
Clothes	31
Clothes	17
Clothes	31
Clothes	20
Food	38
Food	41
Food	42
Food	52
Food	47
Food	42
Food	34
Food	43
Food	57
Food	47
Food	44
Food	54
Toys	53
Toys	44
Toys	48
Toys	56
Toys	63
Toys	53
Toys	48
Toys	58
Toys	47
Toys	51
Toys	51

1. Complete the ANOVA table. Use 0.05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places.)

Source	df	SS	MS	F	p
Factor
Error
Total

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

Level	N	Mean	StDev
Clothes
Food
Toys

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

4. Are there significant differences between pairs of means?

Answer 1

using minitab>stat>ANOVA>one way ANOVA

we have

One-way ANOVA: clothes, 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 clothes, Food, Toys

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 2714 1356.85 22.22 0.000
Error 28 1710 61.07
Total 30 4424

Model Summary

S R-sq R-sq(adj) R-sq(pred)
7.81491 61.34% 58.58% 52.12%

Means

Factor N Mean StDev 95% CI
clothes 9 28.56 10.74 (23.22, 33.89)
Food 12 45.08 6.68 (40.46, 49.70)
Toys 10 51.90 5.74 (46.84, 56.96)

Pooled StDev = 7.81491

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean Grouping
Toys 10 51.90 A
Food 12 45.08 A
clothes 9 28.56 B

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference of Difference SE of Adjusted
Levels of Means Difference 95% CI T-Value P-Value
Food - clothes 16.53 3.45 ( 8.00, 25.06) 4.80 0.000
Toys - clothes 23.34 3.59 (14.46, 32.23) 6.50 0.000
Toys - Food 6.82 3.35 (-1.46, 15.10) 2.04 0.122

Individual confidence level = 98.04%

1. Complete the ANOVA table. Use 0.05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places.)

Source	df	SS	MS	F	p
Factor	30	2714	1356.85	22.22	0.000
Error	28	1710	61.07
Total	30	4424

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

Level	N	Mean	StDev
Clothes	9	28.56	10.74
Food	12	45.08	6.68
Toys	10	51.90	5.74

3. yes since p value is less than 0.05 so we can conclude that there is a difference in the mean attention span of the children for the various commercials

4. yes, there is significant differences between pairs of means as given in graph