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 26 45 60 21 48 51 43 43 43 35 53 54 28 47 63 31 42 53 17 34 48 31 43 58 20 57 47 47 51 51 44 54 Click here for the EXCel Data File 1. Complete the ANOVA table. Use 0.05 significance level. (Round the SS and MS values to 1 decimal place, and Fvalue to 2 decimal places. Leave no cells blank - be certain to enter "O" wherever required. Round the df values to nearest whole number.) Source df SS MS F Factors 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? The hypothesis of identical means can definitely be There is in the mean attention 4. Are there significant differences between pairs of means? the other groups. Clothes have a mean attention span of at least ten minutes

Answer 1

Solution:-

1)

ANOVA
Source of Variation	df	SS	MS	F	P-value	F crit
Factors	2	3182.04	1591.02	35.56	0.00	3.33
Errors	29	1297.46	44.74
Total	31	4479.5

2)

Groups	N	Sum	Mean	Variance	Stdev
Clothes	9	252	28	66.25	8.139
Food	12	557	46.417	38.265	6.186
Toys	11	579	52.636	34.654	5.887

3)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂ = u₃

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

MSB F MSE

F = 35.56

The P-value = 0.000

Interpret results. Since the P-value (0.000) is less than the significance level (0.05), we have to reject the null hypothesis.

Conclusion:-

The hypothesis of identical means can definitely be rejected. There is difference in the mean attention.

4) Clothes have a mean attention span of at least ten minutes less than other groups.

Tukey HSD results

treatments pair	Tukey HSD Q statistic	Tukey HSD p-value	Tukey HSD inferfence
Clothes vs Food	8.8304	0.0010053	** p<0.01
Clothes vs Toys	11.5890	0.0010053	** p<0.01
Food vs Toys	3.1504	0.0832612	insignificant