The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1950 pounds and a standard deviation of 80 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, p, of the cables is now greater than 1950 pounds. To see if this is the case, 27 newly manufactured cables are randomly chosen and testedr and their mean breaking strength is found to be 1980 pounds. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean breaking strength of the newly manufactured cables is greater than 1950 pounds? Assume that the population standard deviation has not changed. Perform a onetailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. and round your responses as specmed below. [If necessary. consult a list of formulas.) A coinoperated drink machine was designed to discharge a mean of 9 ounces of coffee per cup. Suppose that we want to carryr out a hypothesis test to see if the true mean discharge differs from 9. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0: H Y P H1: 3 0 s 2 = : A studyr done on a marriage counseling course showed that the proportion of couples for which the communication program can prevent divorce is 75 9'6. Suppose we have strong reason to believe the proportion is less than 75%, and we carry;r out a hypothesis test. State the null hypothesis HD and the alternative hypotheSis H1 that we would use for this test. Hg: P 7 1 H1: 3 O s C E > 2 = :4: A somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44. We have good reason to suspect that the mean number of hours worked per week by software developers, _|.l, is now greater than 44 and wish to do a statistical test. We select a random sample of software developers and find that the mean of the sample is 46 hours and that the standard deviation is 3 hours. Based on this information, complete the parts below. (a) What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test? l1 7 H : D