# Chi-square Test & Confidence for Difference in Proportions

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3.) The professional golf association measured the putting accuracy of professional golfers playing on the PGA tour and the best amateur golfers playing in the world Amateur Championship. A sample of 1075 6-foot putts by professional golfers found 688 made putts. A sample of 1200 6 foot putts by amateur golfers found 696 made putts.

A.) Estimate the proportion of made 6 foot putts by professional golfers. Estimate the proportion of made 6 foot putts by amateur golfers. Which group had a better putting accuracy?

B.) What is the point estimate of the difference between the proportions of the two populations? What does the estimate tell you about the percentage of putts made by the two groups of golfers?

C.) What is the 95% confidence interval for the difference between the two population proportions? Interpret this confidence interval in terms of the percentage of putts made by the two groups of golfers.

17.) The Wall Street Journal's Shareholder Scoreboard Tracks the performance of 1000 major U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the reinvestment of dividends. Ratings are assigned by dividing all 1000 companies into five groups from a (top20%) B, (next 20%) to E (Bottom 20%) Shown here are the one year ratings for a sample of 60 of the largest companies. Do the companies differ in performance from the performance of the 1000 companies in the shareholder scoreboard? Use a=.05

A=5 B=8 C=15 D=20 E=12

23.) With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage. The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies and 100 employees of large companies.

Health insurance

Size of company yes no Total

Small 36 14 50

Med 65 10 75

Large 88 12 100

A.) conduct a test of independence to determine whether employee health insurance coverage is indecent of the size of the company. Us a=.05. What is the p-value and what is your conclusion?

B.) The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the preceding data to support this conclusion.

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##### Solution Summary

The solution provides step by step method for the calculation of confidence interval for difference in proportions and chi square test for association and goodness of fit. Formula for the calculation and Interpretations of the results are also included.

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