Question

Given a random sample of 15 HW scores with the sample mean 82. If it is known that the HW scores follow normal distribution with standard deviation 5, what is the 95% confidence interval for the mean HW score?

(76.5, 87.5) (77.5, 84.5) (78.5, 85.5) (79.5, 84.5)

Answer 1

Solution :

Given that,

= 82

= 5

n = 15

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (5 / 15)

= 2.5

At 95% confidence interval estimate of the population mean is,

- E < < + E

82 - 2.5 < < 82 + 2.5

79.5 < < 84.5

(79.5 , 84.5)