Question

A psychologist has developed an aptitude test which consists of a series of mathematical and vocabulary problems. They are interested in estimating the mean score for all those who take the test.

A random sample of 31 people have taken the test and the mean test score for the sample is 75. The sample standard deviation for this group is 9.0

Calculate the 95% confidence interval for the mean test score. Give your answers to 2 decimal places.

________ ≤ μ ≤ ________

Answer 1

Solution :

Given that,

= 75

= 9

n = 31

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 * (9 / 31)

= 3.17

At 99% confidence interval mean is,

- E < < + E

75-3.17 < < 75+3.17

71.83< < 78.17