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. 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

The estimated population mean for the number of hours lost due to accidents for the company using a 98% confidence interval is between 94.061 and 99.939 hours. None of the given answer options match the calculated confidence interval, so it seems there may be an error in the provided answer choices.

To estimate the population mean for the number of hours lost due to accidents for the company using a 98% confidence interval, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard deviation / √sample size)

First, let's calculate the critical value. Since we want a 98% confidence interval, we need to find the z-score that corresponds to a 1% (0.01) significance level in the tail of the distribution. This critical value can be found using a z-table or calculator, and for a 98% confidence interval, the critical value is approximately 2.33.

Next, we can substitute the given values into the formula:

Sample mean = 97 hours
Standard deviation = 5.2 hours
Sample size = 17

Confidence Interval = 97 ± (2.33 * 5.2 / √17)

Now let's calculate the confidence interval:

Confidence Interval = 97 ± (2.33 * 5.2 / √17)
Confidence Interval = 97 ± (2.33 * 5.2 / 4.12)
Confidence Interval = 97 ± (12.116 / 4.12)
Confidence Interval = 97 ± 2.939

Finally, we can write the confidence interval as a range:

Confidence Interval = 97 ± 2.939
Confidence Interval = (97 - 2.939) to (97 + 2.939)
Confidence Interval = 94.061 to 99.939

Therefore, the estimated population mean for the number of hours lost due to accidents for the company using a 98% confidence interval is between 94.061 and 99.939 hours.

None of the given answer options match the calculated confidence interval, so it seems there may be an error in the provided answer choices.

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