In: Statistics and Probability
A GSS asked, "What do you think is the ideal number of children
for a family to have?"
For the 555 males in the sample, the mean was 2.89 and the standard
deviation was 1.77.
Find the 95% confidence interval for the population mean.
A. (2.743, 3.037)
B. (2, 3)
C. (3.243, 4.037)
D. (0, 1)
Solution :
Given that,
Point estimate = sample mean = = 2.89
Population standard deviation = =1.77
Sample size n =555
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z/2
* (
/n)
= 1.96 * ( 1.77 / 555 )
= 0.147
At 95% confidence interval mean
is,
- E < < + E
2.89- 0.147 <
< 2.89 + 0.147
(2.743, 3.037)