# A machine that puts corn flakes into boxes is adjusted to put an average of 15.7 ounces into each box, with standard deviation of 0.23 ounce.

15.70.23180.39

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

State the null and alternate hypotheses.

H0: σ2 < 0.0529; H1: σ2 = 0.0529

H0: σ2 = 0.0529; H1: σ2 > 0.0529

H0: σ2 = 0.0529; H1: σ2 < 0.0529

H0: σ2 = 0.0529; H1: σ2 ≠ 0.0529

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

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

P-value > 0.100

0.050 < P-value < 0.100

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(iv) Conclude the test.

Since the P-value ≥ α, we fail to reject the null hypothesis.

Since the P-value < α, we reject the null hypothesis.

Since the P-value < α, we fail to reject the null hypothesis.

Since the P-value ≥ α, 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. 