Final answer:
To construct a 98% confidence interval for the mean salary of high school counselors in the United States, calculate the sample mean and the margin of error. The 98% confidence interval is approximately $46,208 to $57,006.
Step-by-step explanation:
To construct a 98% confidence interval for the mean salary of high school counselors across the United States, we can use the formula:
Confidence Interval = sample mean ± margin of error
First, we need to calculate the sample mean. The sample mean is the average of the salaries in the random sample. In this case, the sample mean is $52,107.14.
Next, we need to calculate the margin of error. The margin of error is the maximum amount that the sample mean is likely to differ from the true population mean. To calculate the margin of error, we can use the formula:
Margin of Error = critical value x standard deviation / square root of sample size
In this case, the critical value for a 98% confidence interval is approximately 2.33. The standard deviation for the sample salaries is $13,707.85, and the sample size is 7. Plugging in these values, we get:
Margin of Error = 2.33 x $13,707.85 / √7 ≈ $5,898.67
Finally, we can construct the confidence interval:
Confidence Interval = $52,107.14 ± $5,898.67
Rounding to the nearest dollar, the 98% confidence interval for the mean salary of high school counselors across the United States is approximately $46,208 to $57,006.