Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the manager's claim.

H0: p = 0.03. H1: p > 0.03. Test statistic: z = 1.57. P-value: p = 0.0582.

Critical value: z = 2.33. Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the manager's claim that production is not really out of control.

H0: p = 0.06. H1: p < 0.03. Test statistic: z = 1.57. P-value: p = 0.0582.

Critical value: z = -3.33. Reject null hypothesis. There is sufficient evidence to warrant rejection of the manager's claim that production is not really out of control.