STAT200 Lesson 7: Confidence Intervals Lab Activity complete solutions correct answers key

STAT200 Lesson 7: Confidence Intervals Lab Activity complete solutions correct answers key

Answer the following questions showing all work. I strongly suggest using Minitab Express to answer questions when possible, as opposed to hand calculations. This will save you time and reduce mathematical errors. When you use Minitab Express, include the appropriate output (copy + paste) along with an explanation.

1. For each of the following, compute the correct degrees of freedom and find the correct t multiplier for constructing a confidence interval for a population mean. You may use the t table or Minitab Express. [20 points]

A. Confidence level 80%, n=9, df = _____, t* = ______

B. Confidence level 80%, n=101, df = _____, t* = ______

C. Confidence level 95%, n=9, df = _____, t* = ______

D. Confidence level 95%, n=101, df = _____, t* = ______

E. How does the t multiplier change as the confidence level changes? Why?

F. How does the t multiplier change as the sample size changes? Why?

G. How does the t multiplier change as the population size changes? Why?

2. For the following scenarios, if you were to construct a confidence interval, what would be the appropriate multiplier?  (State whether z* or t* AND look up the number) [16 points]

A. You want to estimate the proportion of Penn State students who own a Mac with 95% confidence. You take a simple random sample of 56 Penn State students.

B. You want to estimate the average weight of male golden retrievers with 98% confidence.  You have a sample of 26 male golden retrievers.

C. You want to construct a 90% confidence interval for the mean number of credits completed by students enrolled in STAT 200 this semester across all campuses. You take a random sample of 600 students.

D. You want to construct an 80% confidence interval for the proportion of registered Pennsylvanian voters who plan to vote for Candidate A. You take a random sample of 21 registered voters in Pennsylvania.

3. During the first week of class data were collected from a sample of World Campus STAT 200 students.  This data can be found in the file SP16STUDENTDATA.MTW. Use this data to answer the following questions. Copy + paste all relevant Minitab Express output.  Clearly identify your answers. [32 points]

A. What proportion of students in this sample said that they were dieting?

B. Compute a 95% confidence interval for the proportion of the population of all World Campus STAT 200 students who are dieting. Use the normal approximation method.

C. Interpret the confidence interval that you constructed in part (B).

D. In this sample, what were the mean and standard deviation for the variable of height in inches?

E. Compute an 80% confidence interval for the mean height in inches in the population of all World Campus STAT 200 students.

F. Interpret the confidence interval that you constructed in part (E)

G. Compute a 99% confidence interval for the mean height in inches in the population of all World Campus STAT 200 students.

H. Which is wider, the 80% confidence interval in part (E) or the 99% confidence interval in part (G)?  Explain why.

4. You have collected data concerning SAT-Math scores from a sample of 27 Penn State statistics majors. Your sample has a mean of 720 and a standard deviation of 40. [20 points]

A. Construct a 95% confidence interval for the mean SAT-Math score of all Penn State statistics majors.

B. In the general population (i.e., students who are not statistics majors), the mean SAT-Math score is 500.  Given your results from part (A), is there evidence that Penn State statistics majors are different from the general population in terms of their average SAT-Math score? Explain why.

C. If you wanted to construct a 95% confidence interval for SAT-Math score in all Penn State statistics majors with a margin of error of 10 points, what sample size would you need?

D. If you wanted to construct a 95% confidence interval for SAT-Math score in all Penn State statistics majors with a margin of error of 5 points, what sample size would you need?

E. Compare your results from part (C) and part (D). Which is larger? Explain why?

5. The graphics below were published in an NPR article on January 30, 2016. These data were collected just days before the Iowa caucuses.  Use these to answer the following questions.

For the entire article, see http://www.npr.org/2016/01/30/465000699/hillary-clinton-donald-trump-narrowly-ahead-in-final-poll-before-iowa [12 points]

A. The article states, “Hillary Clinton and Donald Trump lead narrowly just two days before the Iowa caucuses in the final Des Moines Register/Bloomberg poll, considered the “global standard” of Iowa polling. But Clinton’s 3-point lead over Vermont Sen. Bernie Sanders is within the margin of error.”  How would you explain what it means to be “within the margin of error” to a friend who in interested in political polling but who has never taken a statistics course?

B. If the only information that you had was the graphs above, would you be convinced that Clinton was going to beat Sanders in the Iowa caucus? Why or why not?  (Assume that the sample is representative.)

C. Given only the information in the graphs above, is there evidence that in the population of all Iowa voters more would select Trump as their first choice than Rubio? (Assume that the sample is representative.)

D. In terms of the actual results, for the republicans, Cruz won with 27.6% of votes and for the democrats Clinton won with 49.9% of votes.  Why are these numbers different from the ones presented in the graphs from the NPR article?