At a large company, the Director of Research found that the average work time lost by employees due to accidents was 97 hours per year. She used a random sample of 17 employees, and the standard deviation of the sample was 5.2 hours.

Estimate the population mean for the number of hours lost due to accidents for the company using a 98% confidence interval.

a) 85.2 < μ < 91.7
b) 95.2 < μ < 100.8
c) 93.7 < μ < 100.3
d) 85.6 < μ < 90.3

To estimate the population mean for the number of hours lost due to accidents, we can use a confidence interval based on the sample mean and the standard deviation of the sample. Given that the sample mean is 97 hours per year and the standard deviation is 5.2 hours, we can calculate the margin of error using the formula:

Margin of Error = Critical value * (Standard deviation / √(Sample size))

Since we want a 98% confidence interval, the critical value is found by subtracting 1 minus the desired confidence level from 1 and dividing it by 2. In this case, (1 - 0.98) / 2 = 0.01.

Next, we substitute the values into the formula:

Margin of Error = 2.33 * (5.2 / √17) ≈ 2.19

Finally, we construct the confidence interval by subtracting and adding the margin of error to the sample mean:

Lower bound = Sample mean - Margin of Error = 97 - 2.19 ≈ 85.6

Upper bound = Sample mean + Margin of Error = 97 + 2.19 ≈ 90.3

Therefore, we estimate that with a 98% confidence, the population mean for the number of hours lost due to accidents for the company lies within the range of 85.6 to 90.3 hours.

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