(10 Points) You run a factory and are contracting with a supplier who ships you important components. You are considering imposing a rule over whether to "accept" a shipment of components or not based on how many of them may be defective. You consider the following two rules: Rule 1: A random sample of ten components is checked, and the shipment is accepted only if none of them is defective. Rule 2: A random sample of 20 components is checked, and the shipment is accepted only if not more than one of them is defective. If a shipment contains 20% defectives, which of these acceptance rules has the smaller probability of accepting the shipment?

Arecent study focused on the number of times men and women who live alone buy take-out dinner in a month. assume that the distributions follow the normal probability distribution and the population standard deviations are equal. the information is summarized below. statistic men women sample mean 24.85 21.33 sample standard deviation 5.54 4.93 sample size 34 36 at the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? state the decision rule for 0.01 significance level: h0: μmen= μwomen h1: μmen ≠ μwomen. (negative amounts should be indicated by a minus sign. round your answers to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? what is the p-value? (round your answer to 3 decimal places.)