Question

A sample of 15 quality control managers with more than 20 years experience have an average salary of $68,000 and a sample standard deviation of $19,000.You can be 95% confident that the mean salary for all quality managers with at least 20 years of experience is between what two numbers? What assumptions are you making about the distribution of salaries?

Answer 1

The mean salary for all quality managers with at least 20 years of experience is between approximately $62,796 and $73,204 at a 95% confidence level.

Step-by-step explanation:

To determine the range within which we can be 95% confident that the mean salary for all quality managers with at least 20 years of experience falls, we can use a confidence interval formula. The formula for the confidence interval is: Sample Mean +/- (Critical Value * Standard Error). The critical value can be found using a t-table or calculator, and the standard error is calculated as the sample standard deviation divided by the square root of the sample size. Substituting the given values into the formula, we can determine the confidence interval range. In this case, the mean salary for all quality managers with at least 20 years of experience is between approximately $62,796 and $73,204 at a 95% confidence level.

The assumptions made about the distribution of salaries in this case are:

1. The sample data is a representative sample of all quality control managers with more than 20 years experience.
2. The distribution of salaries is approximately normal.
3. The sample standard deviation is an accurate estimate of the population standard deviation.