Question 12 of 18 , Step 1 of 1
$16/25$
Correct
3
The following is a random sample of the annual salaries of high school counselors in the United States. Assuming that the distribution of salaries is approximately normal, construct a $99\mathrm{\%}$ confidence interval for the mean salary of high school counselors across the United States. Round to the nearest dollar.
$$\text{Unknown environment 'tabular'}$$
Copy Data
Answer
Tables
Keypad
Keyboard Shortcuts
Lower endpoint:

Upper endpoint:
Submit Answer
- 2023 Hawkes Learning

Step 1 ：Given the salaries of high school counselors in the United States, we are asked to construct a 99% confidence interval for the mean salary.

Step 2 ：The given salaries are: $63670, $35250, $61780, $32370, $32290, $60250, $60590.

Step 3 ：First, we calculate the mean and standard deviation of the given salaries. The mean is $49457.14 and the standard deviation is $14055.04.

Step 4 ：Next, we use the formula for the confidence interval which is mean ± (z-score * (standard deviation / sqrt(n))), where n is the number of samples, and the z-score for a 99% confidence interval is approximately 2.576.

Step 5 ：Substituting the values into the formula, we get the margin of error as $13683.59.

Step 6 ：Finally, we subtract and add the margin of error from the mean to get the lower and upper endpoints of the confidence interval respectively.

Step 7 ：The lower endpoint is $35774 and the upper endpoint is $63141.

Step 8 ：So, the 99% confidence interval for the mean salary of high school counselors across the United States is $\boxed{{\displaystyle [\mathrm{\$}35774,\mathrm{\$}63141]}}$.