Question

Due to pressure from health-conscious consumers and government regulations, there are now many cereals available in grocery stores that claim to be low in sugar. But is there significantly less sugar in these “low sugar” cereals as compared to other cereals that do not claim to be low in sugar? The amount of sugar (in grams) in 10 randomly selected “regular” cereals and 10 randomly-selected “low sugar” cereals are as follows:

Regular = (13, 2, 12, 10, 20, 10, 11, 10, 9, 9)
Low = (10, 1, 9, 8, 18, 8, 10, 8, 4, 8)

(a) State the appropriate null and alternative hypotheses for testing if the variance of “regular” cereals differs from the variance of “low sugar” cereals.

(b) State the appropriate test statistic and p-value for a test of the hypotheses in part (a).

(c) Based on the results of this test and using α = 0.05, can we say that the variances are significantly different?

Answer 1

For this we conduct an F test for 2 variances (Since we want to test variation)

From The data

s₁² = 19.6, n₁ = 10, df₁ = 10-1 = 9

s₂² = 19.12, n₂ = 10, df₂ = 10-1 = 9

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(a) The Hypothesis:

H0: : There is no difference in variation between regular cereals and low sugar cereals.

Ha: : There is a difference in variation between regular cereals and low sugar cereals.

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(b) The Test Statistic:

F = s₁² / s₂² = 19.6 / 19.12 = 1.03

The p value for F = 1.03, degrees of freedom (9,9) is = 0.9656

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The Decision Rule: If p value is < , Then Reject H0.

The Decision: Since p value is > , We fail to Reject H0.

The Conclusion: There isn’t sufficient evidence at the 95% significance level to conclude that there is a significant difference in variance between regular cereals and low sugar cereals.
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