Question

Use EXCEL and DATA ANALYSIS to find the answers to these questions. Provide all EXCEL printouts and 6 step write-ups for each of the two problems.

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
38	30.2
47.4	23.2
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

A)Null Hypothesis,H₀:The variance of sugar content of children's cereals is equal to that of adult's (i.e)

Alternative Hypothesis ,H₁: The variance of sugar content of children's cereals is not equal to that of adult's (i.e)

Level of significance =0.05

Test statistic : F= = 0.6423

Critical value is F_(14,14,0.05)=2.4387

Inference : Since F_cal is less than F_cric , we accept H₀ and conclude that the variance of sugar content of children's cereals is equal to that of adults

B)p value is given as 0.4177

Since p value is greater than 0.05, we accept H₀ which implies (A)

C)Null Hypothesis,H₀:The average level of sugar in cereals of children is less than the average level of sugar in cereals of adults (i.e)

Alternative Hypothesis,H₁:The average level of sugar in cereals of children is higher than that of adults (i.e)

Level of significance =0.05

Test statistic is

From (A), we assume equal variances,then the value of t = 7.822

Critical value is t_28,0.025 = 1.7011

Since t_cal is greater than t _cric, we reject H₀ and conclude that the average level of sugar in cereals of children is higher than that of adults.

D)p value is given as 8.03E-09

Since p value is less than 0.05, we reject H₀ which implies (C)

E)From the results obtained above , we have strong evidence the criticism is true that the sugar levels in cereals of children is different from that of adults and is also high , so the company needs to address to this issue and reduce the level of sugar in the cereals manufactured for children so that it meets the demands although there is no variation is sugar content giving large sugar to children won't be entertained by their parents .

The excel output is