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
34	38	64
30	34	50
44	51	39
35	42	48
28	47	63
31	42	53
17	34	48
31	43	58
20	57	47
	47	51
	44	51
	54

1)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/not rejected.There is a difference/no difference in the mean attention span

  

2)Are there significant differences between pairs of means?

Clothes have a mean attention span of at least ten minutes above/below the other groups

Answer 1

Answer: 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

Solution:

1) From the given data:

Group	n	Σx	mean	Σx^2	Std.Dev
Clothes	9	270	30	8612	8
Food	12	533	44.4167	24253	7.2546
Toys	11	572	52	30278	7.3075
Total	32	1375	42.969	63143	11.4455

Anova table:

Source	df	SS	MS	F	P-VALUE
Factor	2	2436.0521	1218.026	21.7382	0.00001
Error	29	1624.9167	56.0316
Total	3	4060.9688

The hypothesis test:

Null hypothesis, Ho: μ1 = μ2 = μ3

Alternative hypothesis, Ha: at least one of the μ is not equal.

From the ANOVA results:

F test statistic = 21.7382

P-value = 0.00001

Assuming significance level α = 0.05

Since P-value < α (0.05) significance level.

We reject the null hypothesis, Ho.

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

2)

Clothes have a mean attention span of at least ten minutes below the other groups.

If any doubt feel free to ask. If this answer is helpful to you then please upvote.