A firm employs 189 junior accountants. In a random sample of 50 of these, the mean number of hours overtime billed in a particular week was 9.7, and the sample standard deviation was 6.2 hours. Find a 95\% confidence interval for the mean number of hours overtime billed per junior accountant in this firm that week.

UkusakazaL

UkusakazaL

Answered question

2021-08-10

A firm employs 189 junior accountants. In a random sample of 50 of these, the mean number of hours overtime billed in a particular week was 9.7, and the sample standard deviation was 6.2 hours.
a. Find a 95% confidence interval for the mean number of hours overtime billed per junior accountant in this firm that week.
b. Find a 99% confidence interval for the total number of hours overtime billed by junior accountants in the firm during the week of interest.

Answer & Explanation

Ian Adams

Ian Adams

Skilled2021-08-16Added 163 answers

Given data,
The number of employee is 189.
The mean of the overtime is 9.7.
The standard deviation of overtime is 6.2
The sample size is 50.
Step 1
a) A 95% confidence interval for the mean number of hours overtime,
Error margin =z0.052σn
=z0.00256.250
=1.96×0.8768
=1.72
The lower bound of the interval is,
L=μ Error
=9.71.72
=7.98
The upper bound of the interval is,
U=μ+ Error
=9.7+1.72
=11.42
Step 2
b) A 99% confidence interval for the mean number of hours overtime,
Error margin =z0.012σn
=z0.0056.250
=2.576×0.8768
=2.2586
The lower bound of the interval is,
L=μ Error
=9.72.2586
=7.4414
The upper bound of the interval is,
U=μ+ Error
=9.7+2.2586
=11.9586

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