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Statistics HW 7

Statistics HW 7 - Question 1 0.25 out of 0.25 points...

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Question 1 0.25 out of 0.25 points SPECIAL INSTRUCTIONS: PLEASE NOTE!! In this assignment, the proportion of the population who are “successes” will be denoted by the Greek symbol π and the proportion of the sample of size n, who are “successes”, will be denoted by π-hat (π π̂ ) . Remember I use the terms fraction and proportion interchangeably. In the context of statistics their meanings are equivalent. Pepsi claims Texas A&M Central Texas graduate students prefer Pepsi to Coke. To test their claim, I sample 160 graduate students at random from the population of Texas A&M Central Texas graduate students. Let π be the population proportion that prefers Pepsi to Coke. The null hypothesis is H 0 : π = 0.5 (neither Coke nor Pepsi is preferred). Suppose that I observe in my sample that 60 preferred Pepsi. Construct a confidence interval with a given confidence level. Note : There are two ways to do this problem. a. The first is to set up a Minitab data file where the variable is called "Pepsi" and has a sample size of 160. The first 60 observations are labeled Pepsi and the next 100 observations are labeled Coke. Then go to Minitab, use Stat, Basic Statistics, 1- Proportion for this variable. Place the variable in the panel, then select “Perform hypothesis test”, entering 0.5 in the proportion box. Select Options and enter the appropriate confidence level. OR...you could select One-Sample Proportion, select Summarized data in the drop down box and enter your "successes" in the number of events, and the total sample size in the number of trials. On both methods, ensure you select options, enter the appropriate confidence level, and select Normal approximation in the Method drop down box. Always 2-tailed tests. b. Alternatively, you construct the confidence interval by hand (Statistical Calculations in Excel would help you here). Do both methods using 90% and 95% confidence levels. c. Use four (4) significant digits (on the right side of the decimal) for both the hand calculations and the Minitab output. The 90% Confidence Interval using Minitab is (to 4 significant digits): ( [a] , [b] ). Specified Answer for: a 0.31 20 Specified Answer for: b 0.43 80 Correct Answers for: a Evaluation Method Correct Answer Pattern Match 0.312056 Pattern Match 0.31205 Pattern Match 0.3120
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Correct Answers for: b Evaluation Method Correct Answer Pattern Match 0.437954 Pattern Match 0.43795 Pattern Match 0.4380 Question 2 0.25 out of 0.25 points The 95% Confidence Interval using Minitab is (to 4 significant digits): ( [a] , [b] ). Specified Answer for: a 0.30 00 Specified Answer for: b 0.45 00 Correct Answers for: a Evaluation Method Correct Answer Pattern Match 0.29999 Pattern Match 0.299986 Pattern Match 0.3000 Correct Answers for: b Evaluation Method Correct Answer Pattern Match 0.45001 Pattern Match 0.450014 Pattern Match 0.4500 Question 3 0.25 out of 0.25 points Do we reject the null hypothesis with 90% confidence?
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  • Summer '16
  • Rick Simmons
  • Evaluation Method, Statistical hypothesis testing, Pearson's chi-square test, Pattern Match

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