3. Confidence Interval: You operate a quality control company that evaluates the

Question

3. Confidence Interval: You operate a quality control company that evaluates the operational quality of slot machines that are distributed through your partner vendor. For each slot machine that you test, the expected loss (gain for the casino) is 10 cents per $1 bet. In order to test each machine, you run 1000 bets and calculate the amount that a hypothetical player would receive as a payout. For each bet, the player either wins $5 or loses a. Compute a 95% confidence interval for the average loss per bet for the outcomes below (i-iii), which slot machines (if any) would you suspect as being defective? If you suspect a machine to be defective, state your level of confidence. Note: A machine is defective if it deviates significantly from an expected loss of 10 cents per game. Payout = $1250 (net winnings-$250) ii. Payout $1100 (net winnings $100) iii. Payout = $700 (net winnings--$300) b. Repeat (a) using a 95% confidence interval of the proportion of winning games. Compare your results with those obtained in (a) and (b). Note: The proportion of games that a player can expect to win for a non-defective slot machine is 18%.

Explanation / Answer

4

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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