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hw4soln

# hw4soln - Problem No 1(a A manufacturer of VCR systems...

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Problem No. 1 (a) A manufacturer of VCR systems would like to estimate the mean failure time of a VCR brand with 95% confidence. Six systems are tested to failure, and the following data (in hours of playing time) are obtained: 1250, 1320, 1542, 1464, 1275, and 1383. Estimate the population mean and the 95% confidence interval on the mean. (This a small number of data points so you will want to use the Student’s t function for these estimates). (b) To reduce the 95% confidence interval to ± 50 hours, the VCR manufacturer decides to test more systems to failure. Determine how many more systems should be tested. (If this is a small number you may need to iterate with the Student’s t function to arrive at you answer). Solution (a): Because the sample size is small (n < 30), we should use the t-distribution to estimate the confidence interval. But first we have to calculate the mean and (sample) standard deviation of the data. x mean 1250 1320 + 1542 + 1464 + 1275 + 1383 + 6 := x mean 1.372 10 3 × = hours x x mean := S 1250 x ( ) 2 1320 x ( ) 2 + 1542 x ( ) 2 + 1464 x ( ) 2 + 1275 x ( ) 2 + 1383 x ( ) 2 + 6 1

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hw4soln - Problem No 1(a A manufacturer of VCR systems...

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