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Baseball, Record Store and College Admin Probabilities

Problem #4

Historically, the Giant's opening home game has been on a Sunday with an average crowd of 60,000. During the last 5 years, they have opened on Saturday with an average crowd of 58,000. Allowing a 2,5% error of type 1, formally test the hypothesis that opening on Saturday has dampened attendees. S =S/vn=1000

Suppose the average home opener crowd has actually fallen to 59,000. What is the probability of erroneously accepting the belief that the opening day attendance has not been impacted by what day of the weekend the game is played?

Problem #5

Tower Records historically sells 500 CDs per day in its Midtown store. Store traffic has increased as a result of the Tomes Square redevelopment, and Tower management believes business has improved. With a 5% probability of being in error, test the belief that Tower's business has improved. A sample of 100 sales days generated an average sales figure of 512 CDs per day with a sample standard deviation S=36 CDs.
If average daily sales have risen to 508 CDs, what is the probability the management will erroneously conclude that business has remained unaffected by the Times Square development?

Problem #6

In the Tower Records situation of problem 5 above, suppose another record store opens in the neighborhood of tower. Even though store traffic has increased, so has the competition. With a 5% probability of being in error, now test the notion that Tower's business has changed in some fashion as a result of the Times Square buildup. (All other aspects of the story in problem 5 still apply).

Formally calculate the probability of type II error ( B-error)under this second scenario.

Problem #7

Collage administrators believe that high school graduates' SAT performance has exhibited increased variability/ dispersion over the past decade. Historically the variance in SAT scores has been 100 points. But, administrators believe that SAT score variance has increased relative to the historical norm. A sample of 50 test scores was taken generating a sample variance of 110 points. Allowing a 5% probability of a type-I error. Formally test the conjecture that the variance in SAT scores has widened from the historical norm.

Solution Summary

Excel attachment tackles these three problems of mistaken statistical conclusions.