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Confidence interval calculation

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A car manufacturer has redesigned the anti-theft device on one of its models to increase the time that it takes for a professional car thief to be able to steal the car. To determine the length of time that it takes it employs 30 reformed criminals to see how long it takes to steal the car. The sample has a mean time of 6 minutes and a standard deviation of 2 minutes.

i) Calculate a 95% confidence interval for the mean length of time it will take a
car thief to steal the car.

ii) Calculate the size of the sample required so that the margin of error for the
95% confidence interval is 0.5.

Please do not use excel functions - I would like to see clear workings and commentary for calculations

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Solution Preview

a) At 95% level and df=n-1=30=1=29, the critical value is 2.0452 .
So 95% confidence ...

Solution Summary

The solution gives detailed steps on computing the confidence interval. All formula and calculations are shown and explained.