REIDS NOTES

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Binghamton University *

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MISC

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Statistics

Date

Jan 9, 2024

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docx

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Notes/Examples for Mr. Reid’s Bootstrapping Video 1. A sample of security system and equipment contracts for a large company were collected and the commission earned by the employee submitting the bid was recorded. These commission values are below: 220, 900, 1800, 4000, 2500, 7000, 350, 4100, 3800, 2500, 2100, 2800, 3300, 2000, 700, 1500, 4000, 5100, 3900, 2100, 1750, 3000 a. What does the bootstrap distribution look like? Can we use the 2 standard error rule to get a 95% confidence interval? The distribution looks like a bell shaped distribution. Yes we can. b. Give the interval and interpret it. 2694.865 +/- 2(331.597) 2694.865 +/- 663.194 (2031.67, 3358.06) We are 95% sure that the population mean sales contract commission is between $2031.68 and $3358.06 c. A golf club had 2 courses, a blue course and an orange course. In a sample of golfers, the course and the score were recorded. This data is given in the Excel file, “Golf Scores by Course”. Suppose we were interested in getting a confidence interval estimate for the difference in means. a. What is the parameter we are trying to estimate? μ0 -μb

b. What sample statistic will we have? x̄ 0-x̄ b c. In StatKey, do the bootstrapping method. Can we use the 2 SE approach? Yes d. What is the interval? Interpret it. Stat +- 2 SE (-0.520, 10.148) We are 95% sure the difference in population mean golf scores between the courses is between -.52 and 10.148 e. What does this suggest? Using a 95% confidence level there might not be a difference in population mean scores. 1. In a sample of 123 cell phones of brand A, 89 survived a fall of 10 feet without damage. From brand B, 71 out of 145 phones survived the same fall. a. Sketch the bootstrap distribution: b) Construct the 95% confidence interval – interpret it. Statistics +/- 2(SE) 0.234 +/- 2(0.058)

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