Question

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 90% confidence interval for the mean salary of high school counselors across the United States. Round to the nearest dollar.

$55,250, $46,540, $42,120, $58,740, $38,010, $43,650, $65,640

Answer 1

Solution :

Given that 55250, 46540, 42120, 58740, 38010, 43650, 65640

=> Mean x-bar = sum of terms/number of tems

= 349950/7

= 49992.8571

= 49993 (nearest integer)

=> Standard deviation s = 10055.7442

= 10056 (nearest integer)

=> df = n - 1 = 6

=> for 90% confidence interval, t = 1.943

=> A 90% confidence interval for the mean salary of high school counselors across the United States is

=> x-bar +/- t*s/sqrt(n)

=> 49993 +/- 1.943*10056/sqrt(7)

=> (42608.0247 , 57377.9753)

=> (42608 , 57378) (nearest integer)