A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. Calculator The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking (These samples are chosen independently.) For the people taking Ripped, their sample mean is 9.76 with a sample variance of 11.67. For the people takıng Gainz, their sample mean is 7.84 with a sample variance of 1.38. Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.10 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

A psychology student conducted a study on using a chief executive​ officer's facial structure to predict a​ firm's financial performance. The facial​ width-to-height ratio​ (WHR) for each in a sample of 47 CEOs at publicly traded firms was determined. The sample resulted in x=2.23 and s=0.35. The student wants to predict the financial performance of a firm based on the value of the true mean facial WHR of CEOs. The student wants to use the value of μ=2.1. Do you recommend he use this​ value? Conduct a test of hypothesis for μ to help you answer the question. Specify all the elements of the​ test, including H0​, Ha​, test​ statistic, p-value, and your conclusion. Test at α=0.01.

Given a data point x, what does the z-score tell us about x?

The blue catfish (Ictalurus Furcatus) is the largest species of North Amercian catfish. The current world record stands at 143 pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to Amercian Expedition, the average weight of a blue catfish is between 20 to 40 pounds. Given that the largest blue catfish ever caught was at the John H. Kerr Reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. Use the data below, which represents the summary statistics for 50 blue catfish caught at this reservoir, and a 0.05 significance level to test the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds. n=50;  ¯x=40.72 pounds;  s=5.03pounds Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal…