A machine that puts corn flakes into boxes is adjusted to put an average of15.7ounces into each box, with standard deviation of0.23ounce. If a random sample of18boxes gave a sample standard deviation of0.39ounce, 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.)

(i) Give the value of the level of significance.

State the null and alternate hypotheses.

H₀:²H₁:²= 0.0529

H₀:²= 0.0529;H₁:²> 0.0529

H₀:²= 0.0529;H₁:²

H₀:²= 0.0529;H₁:²0.0529

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

(iii) Find or estimate theP-value of the sample test statistic.

P-value > 0.100

0.050 P-value

0.025 P-value

0.010 P-value

0.005 P-value

P-value

(iv) Conclude the test.

Since theP-value, we fail to reject the null hypothesis.

Since theP-value , we reject the null hypothesis.

Since theP-value , we fail to reject the null hypothesis.

Since theP-value, we reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is sufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.

At the 1% level of significance, there is insufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.