The 1996 GSS asked, \"If the husband in a family wants children, but the wife de
ID: 3062947 • Letter: T
Question
The 1996 GSS asked, "If the husband in a family wants children, but the wife decides that she does not want any children, is it all right for the wife to refuse to have children?" Of 716 respondents, 564 said yes. (a) Find a 99% confidence interval for the population proportion who would say yes. Round to two decimal places. Lower Limit Upper Limit Can you conclude that the population proportion exceeds 75%? why? O Yes, this interval lies above 0.75 O No, this interval lies below or contains 0.75 O There is not enough information. (b) Without doing any calculation, would the interval in (a) be wider or narrower than a 94% confidence interval for the population proportion who would say yes? The 99% confidence interval would be wider than the 94% confidence interval. O The 99% confidence interval would be narrower than the 94% confidence interval.Explanation / Answer
Solution:- Given that N = 716 , X = 564
=>. p = X/N = 564/716 = 0.79 , q = 1-p = 1-0.79 = 0.21
99% confidence for Z = 2.58
a) 99% confidence interval for the proportion : p +/- Z*sqrt(pq/n)
: 0.79 +/- 2.58*sqrt(0.79*0.21/716)
: 0.75 , 0.83
Lower limit : 0.75
Upeer limit : 0.83
=> option B.
b) option A. the 99% confidence interval would be wider than a 94% confidence interval
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