A --test is to be performed for a population mean. Express the decision criterion for the hypothesis test in terms of x. That is, determine for what values of x the null hypothesis would be rejected. After training intensively for six months, John hopes that his mean time to run 100 meters has decreased from last year's mean time of 11.8 seconds. He performs a hypothesis test to determine whether his mean time has decreased. Preliminary data analyses indicate that it is reasonable to apply a -test. The hypotheses are H.:u= 11.8 seconds H:u< 11.8 seconds Assume that o= 0.45 seconds, n=20, and the significance level is 0.03. Express the decision criterion for the hypothesis test in terms of x.

A sociologist claims that the students’ college GPA’s in unrelated to their families’ incomes. For a random sample of 20 students the coefficient of correlation was computed as 0.40. Using the 0.01 significance level, do the formal hypothesis test.Remember to show your steps (including all relevant information) show the steps on how to solve it

Suppose that we are interested in comparing the academic success of college students who belong to fraternal organizations and the academic success of those who do not belong to fraternal organizations. Random samples of size 40 are taken from each population where the variances and standard deviations are known. Sample Size Mean GPA Variance (2) 2.03 2.21 Fraternity member (f): 40 Nonmembers (n): 40 .46 .35 Construct a 96% confidence interval estimate for the difference between the mean GPAS (uf- un). Interpret this interval estimate. What can you conclude about the mean GPAs of the two groups?

Cadmium, a heavy​ metal, is toxic to animals.​ Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. Some governments have a safety limit for cadmium in dry vegetables at 0.56 part per million​ (ppm). A research team measured the cadmium levels in a random sample of edible​ mushrooms, where the hypothesis test is to decide whether the mean cadmium level in the sample is greater than the​ governments' safety limit. The null and alternative hypotheses are H0​: μ=0.56 ​ppm, Ha​: μ>0.56 ppm. Complete parts​ (a) through​ (e) below. d. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms equals the safety limit of 0.56 ppm. Choose the correct answer below. A. type I error B. correct decision because a true null hypothesis is not rejected C. correct decision because…