A pharmaceutical company wanted to estimate the population mean of monthly sales for their 250 sales people. Forty sales people were randomly selected. Their mean monthly sales was $10,000 with a population standard deviation of $1000. Construct a 95% confidence interval for the population mean.

Answer: Between $9,690.1 and $10,309.9 monthly

Explanation:

To calculate confidence interval, we apply this formula:

M ± Z * (σ/√N)

Where M is sample mean; Z is the appropriate value given in the standard normal distribution table at various confidence levels. At 95% confidence level, Z is 1.96. σ population standard deviation; N is sample size.

We know that sample mean is 10,000; sample size is 40; population standard deviation is 1000. We substitute relevant values into the formula

=10,000 ± 1.96 (1000/√40)

=10,000 ± 309.903

Note that 309.903 is referred to in statistics as the margin of error

Thus, the lower limit of 95% confidence interval of the population mean given these values is

10000 - 309.903 = $9,690.097

Thus, the upper limit of 95% confidence interval of the population mean given these values is 10000 + 309.903 = $10,309.903

Statistical interpretation of this result is that we are 95% confident that the average sales per sale person in the pharmaceutical company lies between $9,690.1 and $10,309.9 monthly.