4. Sample Size Determination: You operate a quality control company that evaluat

Question

4. Sample Size Determination: You operate a quality control company that evaluates the operational quality of slot machines that are then sent out to your partner vendor. You find that your current testing methodology works well (run 1000 bets and evaluate outcome) in determining if a slot machine is highly defective, but is poor at determining smaller deviations that can add up rapidly in a casino! You decide to increase the total number of bets you initially examine in your quality control procedure. a. For a defective slot machine, suppose that the true proportion of winning bets is 17.5%. How many the time? For a defective slot machine, suppose that the true proportion of winning bets is 16%. How many bets should you examine so that the 95% confidence interval of p excludes p=0.18 greater than 99% of the time? b.

Explanation / Answer

This question is about sample sizes and marginf of error , we are asked the margin of error to be within 0.01

we know that for 95% CI the value is 1.96 , so the margin of error is given as

Z0.05/2*(p*(1-p)/n)1/2 = 0.01 where p =0.175

Z0.025*(0.144/n)1/2 = 0.01 => 1.96*(0.144/n)1/2 = 0.01

Z0.05/2*(p*(1-p)/n)1/2 = 0.01 where p =0.16

Z0.025*(0.134/n)1/2 = 0.01 => 1.96*(0.134/n)1/2 = 0.01

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