Question

There are 300 students enrolled in Business Statistics. Historically, exam scores are normally distributed with a standard deviation of 26.7. Your instructor randomly selected a sample of 40 examinations and finds a mean of 64.2. Determine a 90% confidence interval for the mean score for all students taking the course. 90% CI = to

Answer 1

Solution :

Given that,

= 64.2

= 26.7

n = 40

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z_/2* ( /n)

= 1.645 * ( 26.7/ 40)

= 6.9446

At 90% confidence interval estimate of the population mean is,

- E < < + E

64.2 - 6.9446 < < 64.2 + 6.9446

57.2554< < 71.1446

(57.2554 to 71.1446 )