A GSS asked, "What do you think is the ideal number of children for a family...

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)

Solutions

Expert Solution

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 * ( / $\sqrt$ n)
= 1.96 * ( 1.77 / $\sqrt$ 555 $\sqrt$ )

= 0.147
At 95% confidence interval mean
is,

- E < < + E

2.89- 0.147 < < 2.89 + 0.147
(2.743, 3.037)

orchestra answered 1 year ago

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