Question

Thirty randomly selected students took the calculus final. If the sample mean was 75 and the standard deviation was 7.2​, construct a​ 99% confidence interval for the mean score of all students.

Answer 1

Solution :

Given that ,

mean = = 75

standard deviation = = 7.2

n = 30

Sample size = n =30

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576* ( 7.2/ 30)

= 3.39

At 99% confidence interval is,

- E < < + E

75-3.39< < 75+3.39

71.61 < < 78.39