Question

 

A food company is concerned about recent criticism of the sugar content of their children’s cereals. The data show the sugar content (as a percentage of weight) of 15  national brands of children and adult cereals.

Children’s Cereal’s	Adult’s Cereal
40.3	20.5
55	30.2
45.7	22.2
43.3	27.5
50.3	34.4
45.9	22.2
53.5	16.6
43	14.5
44.2	21.4
44	30.2
47.4	19.1
44	40.8
33.6	38.1
55.1	21.4
48.8	29.1

1) At the .05 level of significance, is there evidence of a difference in the variance of the sugar content of children’s and adults cereals? Assume that the population values are normally distributed?

2) Provide the p-value for part a) and explain its meaning in words.

3) At the .05 level of significance, is there evidence that children’s cereals contain a higher average level of sugar than adult cereals? Assume that the population values are normally distributed?

4) Provide the p-value for part b) and explain its meaning in words.

5) Write a brief memo regarding what you have decided about the sugar content of children’s and adult’s cereals based on your findings above.

Answer 1

	Children	Adult
Mean	46.3	25.88
Variance	33.36	60.90029
Observations	15	15

1) Two variance test:

The test statisitc:

b) P-value: 0.136087

The test statisitc is not significant and failed to reject H0. There is insufficient evidence to support the claim that there is a diffeence in tha variance of the sugar content and adults cerels.

c) Two sample t-test for equal variance:

The test statistic:

Pooled variance:

4) P-value: 0.0000

The test statisitc is significant and rejects H0. There is sufficient evidence to support the claim that children’s cereals contain a higher average level of sugar than adult cereals.

5) Sugar content of childer's has significantly higher than adult's cereals abased on data.