Question

Wheaties cereal is claimed to have an average of 3 grams of dietary fiber per serving. We want to test this hypothesis and to see whether we believe that is true or that the mean amount of fiber is significantly different from 3 grams. A random sample of 25 servings was taken and it yielded a sample mean of 3.4 grams with the sample standard deviation in the amount of fiber, s = .8 grams.

Assume that software has determined the p-value to be.02.
What would your decision be on this hypothesis test if everything is the same except that we change the level of significance for the test to.01?
Fail to reject the null hypothesis at the 1% level of significance.
Reject the null hypothesis at the 1% level of significance,

Answer 1

The calculated value t = 2.5>2.326 at 0.01 level of significance

The null hypothesis is rejected at a 0.01 level of significance.

Wheaties cereal is not claimed to have an average of 3 grams of dietary fiber per serving

Explanation:

Step(i):-

Given that the average of dietary fiber per serving μ = 3 grams

Given that the mean of the sample x⁻ = 3.4 grams

Given that the standard deviation of the sample (S) = 0.8 grams

Level of significance = 0.01

Critical value = 2.326

Step(ii):-

Null hypothesis: H₀: μ = 3 grams

Alternative Hypothesis: H₁: μ ≠ 3 grams

Tets statistic

`t = (x^(-)-mean )/((S.D)/(√(n) ) )`

`t = (3.4-3 )/((0.8)/(√(25) ) )`

t = 2.5

The calculated value t = 2.5>2.326 at 0.01 level of significance

The null hypothesis is rejected at a 0.01 level of significance.

Final answer:-

Wheaties cereal is not claimed to have an average of 3 grams of dietary fiber per serving