Question

he 2012 General Social Survey asked, “What do you think the ideal number of childrenfor a family to have?” The 590 females who gave a numeric response from 0 to 6 had a median of 2,mean of ̄x= 2.56, and standard deviation ofs= 0.84.a) Two assumptions of confidence interval is : random sample, normal population. General SocialSurvey used a random sample. Do you think this population distribution of ”ideal number ofchildren” satisfy the normality assumption? Why or why not?b) What is the point estimate of the population mean?c) Find the standard error of the sample mean.d) The 95% confidence interval is (2.49, 2.62). Interpret.e) Based on the confidence interval (2.49, 2.62), is it plausible that the population meanμ= 2?Explain.f) Based on the confidence interval (2.49, 2.62), is it plausible that the population meanμ= 2.5?Explain.g) For males, the 95% confidence interval is (2.43, 2.59). Based on two confidence intervals, canwe conclude that males and females have different means? (Hint: When two intervals overlap,we can’t conclude that the two population means are different. (In statistics, “not (significantly)different”6= ”the same”)h) Find the 98% confidence interval for the population mean number of ideal children for females.

Answer 1

a)

for normal distribution mean = median

in our case mean is not same as median so we cannot use normality assumption here.

b)

point estimate of population mean = 2.56

c)

sample mean 'x̄=	2.56
sample size   n=	590
sample std deviation s=	0.84
std error 'sx=s/√n=	0.0346

d)

for 95% CI; and 589 df, value of t=		1.963999758
margin of error E=t*std error    =		0.067919536
lower bound=sample mean-E =		2.492080464
Upper bound=sample mean+E =		2.627919536
from above 95% confidence interval for population mean =(2.4921,2.6279)

we are allowed to solve four sub parts only.