Question

Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use Minitab Express or StatKey include the appropriate output (copy + paste). If you do any hand calculations show your work using the Word equation editor. Clearly identify your final answers. Output without explanation will not receive full credit and answers with no output or explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board.

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

A. State the null and alternative hypotheses that the researchers should test. Use m_d to denote the mean weight loss computed as beginning weight minus final weight.

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

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

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

E. If you were working with this research team, what alpha level would you use? Explain your reasoning.

Assume that the research team completes this study with a sample size of 500 and finds a mean weight loss of 0.475 pound with a standard deviation of 3.978 pounds. Their p-value is 0.0039

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

G. Are their results practically significant? Explain why or why not.

2. The STAT 200 course coordinator wants to estimate the proportion of all online STAT 200 students who utilize Penn State Learning’s online tutoring services by either attending a live session or viewing recordings of sessions. In a survey of 80 students during the Fall 2018 semester, 29 had utilized their services. 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 coordinator decides that she wanted to conduct a hypothesis test instead. She wants to know if the proportion who utilize Penn State Learning’s online tutoring services is different from 0.25. What would be the appropriate null and alternative hypotheses?

B. Based on the 95% bootstrap confidence interval, would you expect the coordinator to reject or fail to reject the null hypothesis from part A at the 0.05 alpha level? Do NOT conduct the hypothesis test; use the confidence interval given in the question. Explain your reasoning.

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

Answer 1

Hi, I am helping you with Q2 ...

(a) Here, the hypotheses would be

Ho: The proportion of students using Penn State Learning’s online tutoring services is 0.25 or less (p ≤ 0.25)

Ha: The proportion of students using Penn State Learning’s online tutoring services is more than 0.25 (p > 0.25)

(b) The confidence interval that was calculated does not include 0.25 and the whole interval is above 0.25. This means the null hypothesis that p ≤ 0.25 has to be rejected, and it should be concluded that more than 25% of the students use the tutoring services

(c) Confidence intervals and hypothesis testing are both used as tools for inferential statistics. They complement each other in the sense that they give the same end conclusion. So, either can be used in statistical analysis. Strictly speaking, a confidence interval is not a test. It's just a range of values within which we can confidently say the true population parameter lies. However, we can do more with a confidence interval than with a hypothesis test. For example, if a t-test doesn't reject the null then we can just say that we can't reject the null, which isn't saying much. But if we have a narrow confidence interval around the null then we can suggest that the null, or a value close to it, is likely the true value and suggest the effect of the treatment is too small to be meaningful or that our experiment doesn't have enough power and precision to detect an effect important to us because the CI includes both that effect and 0.