Question

79. The manufacturer of a machine to package soap powder claimed that her machine could load cartons at a given weight with a range of no more than .4 ounce. The mean and variance of a sample of eight 3-pound boxes were found to equal 3.1 and .018, respectively. Test the hypothesis that the variance of the population of weight measurements is σ 2 = .01 against the alternativethatσ2 >.01.

    1. a Use an α = .05 level of significance. What assumptions are required for this test?

    2. (b) construct the rejection region for this test and make the decision using α = 0.05. (The number is

       easy to calculate, please do the calculation and give the final results. The quantiles might be needed:

       χ27,0.95 = 14.0671, χ27,0.05 = 2.16725, χ28,0.95 = 15.5073, χ28,0.05 = 2.73264, they are all lower tail quantiles).

       (c) Show the formula for calculating formula for p-value of this test. Given that χ27,0.95 = 14.0671 and χ27,0.9 = 12.0170, what’s the range of this p-value? Can we reject the null hypothesis at 0.1 significance level?

Answer 1

The questions is not clearly given hence solving for alpha = 0.05 and 0.01

a. Assumptions : the sample must be taken from a population that is normal.

b

Level of significance = 0.05

Reject Ho: test stat > 14.0671

c.Level of significance = 0.01

We fail to rejec the null hypothesis at alpha = 0.01