Answer the following questions showing all work. Fullcredit will not be given to answers without work shown. If you useMinitab Express or StatKey include the appropriate output (copy +paste). If you do any hand calculations show your work using theWord equation editor. Clearly identify your final answers. Outputwithout explanation will not receive full credit and answers withno output or explanation will not receive full credit. Round allanswers to 3 decimal places. If you have any questions, post themto the course discussion board.

1. A team of researchers has developed a new weight losssupplement. They want to know if patients who use the newsupplement for four weeks lose any weight. The supplement has someminor side effects including mild headaches and achiness. If theresearchers obtain evidence of weight loss they will proceed toproduce the supplement commercially and sell it for a large profit.If they do not obtain evidence of weight loss they will end theproject. [70 points]

A. State the null andalternative hypotheses that the researchers should test.Use m_dto denote the mean weight loss computed as beginning weightminus final weight.

B. What does a Type I errormean in this situation? What are the consequences of making a TypeI error here?

C. What does a Type II errormean in this situation? What are the consequences of making a TypeII error here?

D. In this scenario, is a TypeI or Type II error more serious? Or, are they equally serious?Explain your reasoning.

E. If you were working withthis research team, what alpha level would you use? Explain yourreasoning.

Assume that the research team completes this study witha sample size of 500 and finds a mean weight loss of 0.475 poundwith a standard deviation of 3.978 pounds. Their p-value is0.0039

F. Using the alpha level youselected in part E, are their results statistically significant?Explain why or why not.

G. Are their resultspractically significant? Explain why or why not.

2. The STAT 200 course coordinator wants to estimate theproportion of all online STAT 200 students who utilize Penn StateLearning’s online tutoring services by either attending a livesession or viewing recordings of sessions. In a survey of 80students during the Fall 2018 semester, 29 had utilized theirservices. She used bootstrapping methods to construct a 95%confidence interval for the population proportion of [0.263,0.475]. Use this information to address the following questions.[30 points]

A. Supposed the coordinatordecides that she wanted to conduct a hypothesis test instead. Shewants to know if the proportion who utilize Penn State Learning’sonline tutoring services is different from 0.25. What would be theappropriate null and alternative hypotheses?

B. Based on the 95% bootstrapconfidence interval, would you expect the coordinator to reject orfail to reject the null hypothesis from part A at the 0.05 alphalevel? Do NOT conduct the hypothesis test; use the confidenceinterval given in the question. Explain yourreasoning.

C. Using this scenario,compare and contrast confidence intervals and hypothesis testing.List at least one similarity and at least onedifference.