Question

A sample of 27 employees for the Department of Health and Human Services has the following salaries, in thousands of dollars. Assuming normality, use Excel to find the 98% confidence interval for the true mean salary, in thousands of dollars. Round your answers to two decimal places and use increasing order.

a) 102.36102.36 to 121.29121.29
b) 94.7294.72 to 111.58111.58
c) 116.21116.21 to 134.50134.50
d) 89.1589.15 to 107.94107.94

Answer 1

To find the 98% confidence interval for the true mean salary, calculate the sample mean, standard deviation of the sample, margin of error, and then use the formula (sample mean - margin of error, sample mean + margin of error).

Step-by-step explanation:

To find the 98% confidence interval for the true mean salary, we can use the formula: (sample mean - margin of error, sample mean + margin of error). First, we need to find the sample mean, which is calculated by summing all the salaries and dividing by the sample size. Next, we need to find the standard deviation of the sample, which can be calculated using the formula: (√(sum of (salary - sample mean)^2) / (sample size - 1)). Finally, we can calculate the margin of error using the formula: (critical value * (standard deviation / √sample size)). The critical value can be obtained from a standard normal distribution table or using Excel's NORMINV function. Plugging in the values into the formula will give us the confidence interval.