Question

The 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.

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

(e) Since 2 is not in the confidence interval, it is not plausible that the population mean, μ= 2.

(f) Since 2.5 is in the confidence interval, it is plausible that the population mean, μ= 2.5.

(g) Since the confidence intervals overlap, we can’t conclude that the two population means are different

(h) The 98% confidence interval is:

= 2.56 2.33*(0.84/590)

= 2.48, 2.64

The 98% confidence interval for the population mean number of ideal children for females is between 2.48 and 2.64.

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