Question

A machine that puts corn flakes into boxes is adjusted to put an average of 15.6 ounces into each box, with standard deviation of 0.22 ounce. If a random sample of 12 boxes gave a sample standard deviation of 0.38 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.)

(ii) Find the sample test statistic. (Round your answer to two decimal places.)

Answer 1

Given:

Sample size, n = 12

Sample standard deviation, s = 0.38

Population standard deviation, = 0.22

Significance level, = 0.01

Hypothesis test:

The null and alternative Hypothesis :
Null Hypothesis, H0 : σ = 0.22
Alternative Hypothesis, Ha : σ > 0.22

P-value corresponds to test statistics 32.82 with df = 12-1 = 11 is 0.00056.

Since P value is less than significance level, = 0.01 we reject null hypothesis, H0

Hence, data support the claim that the variance has increased and the machine needs to be brought back into adjustment.