According to fueleconomy.gov, the 2018 Toyota Prius Eco 1.8 L, 4-cylinder, automatic with regular gasoline gets 53 highway miles per gallon (Source). However, an independent organization believes that the gas mileage of the Prius is significantly greater than this. In order to test this they collect a random sample of 9 2018 Priuses with these same specifications and measure the highway gas mileages of each. The results of the 9 cars tested are as follows: 52, 54, 59, 59, 53, 56, 57, 55, and 52. If you perform this test at the alpha=0.05 level, state the p-value and the conclusion of the test.

A researcher conducts a study to investigate whether the obesity rate rural communities differ from the obesity rate from the population at large. He gathered a sample of adults from a small community, measured their weight, and compared it to the population average. What statistical test is appropriate for this study and why?

A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that can hold up to 16 ounces of ice cream. The food service manager is interested in comparing the average amount of ice cream dispensed by male students to the average amount dispensed by female students. A measurement device was placed on the ice cream machine to determine the amounts dispensed. Random samples of 85 male and 78 female students who got ice cream were selected. The sample averages were 7.23 and 6.49 ounces for the male and female students, respectively. Assume that the population standard deviations are 1.22 and 1.17 ounces, respectively. Using the 1% significance level, can you conclude that the average amount of ice cream dispensed by male college students is larger than the average amount dispensed by female college students?   What is the type of test to be used?

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…