Question

150 subjects in a psychological study had a mean score of 36 on a test instrument designed to measure anger. The standard deviation of the 150 scores was 12. Find a 95% confidence interval for the mean anger score of the populations from which the sample was selected.

Select one:

a. (32.7, 39.3)

b. (33.2, 38.8)

c. (32.1, 39.9)

d. None of other answer is necessary true.

Answer 1

Solution:
Given that, x̄=36, s =12, n=150
(1–α)%=95%
α=0.05
α/2=0.025
t(α/2),(n-1)=t(0.025),(149)
=1.976 ....from standard normal table.
Margin of error=E= t(α/2),(n-1)×(s/√n)
=1.976 ×(12/√150)
=1.9361
Margin of error=E=1.9361
95% confidence interval for the population mean is given as,
x̄± Margin of error=(36-1.9361,36+1.9361)
=(34.0638,37.9361)

Answer: d) none of other answer is necessary true.