Question

A machine that puts corn flakes into boxes is adjusted to put an average of 15.1 ounces into each box, with standard deviation of 0.26 ounce. If a random sample of 17 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.) (i) Give the value of the level of significance. State the null and alternate hypotheses. H0: σ2 = 0.0676; H1: σ2 ≠ 0.0676 H0: σ2 = 0.0676; H1: σ2 < 0.0676 H0: σ2 < 0.0676; H1: σ2 = 0.0676 H0: σ2 = 0.0676; H1: σ2 > 0.0676 (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.

Answer 1

** (iv) Since the P-value < α, we reject the null hypothesis.

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