A credit card company claims that the mean credit card debt for individuals is greater than $ 5000. You want to test this claim. You find that a random sample of 30 cardholders has a mean credit card balance of $ 5202 and a standard deviation of $ 600. At alpha equals 0.01​, can you support the​ claim? Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.

A random sample of 75 eighth grade​ students’ scores on a national mathematics assessment test has a mean score of 278. This test result prompts a state school administrator to declare that the mean score for the​ state’s eighth graders on this exam is more than 275. Assume that the population standard deviation is 36. At alphaequals0.12​, is there enough evidence to support the​ administrator’s claim? Complete parts​ (a) through​ (e).

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