According to a 2011 opinion poll by Ipsos Public Affairs, 75% of American teens

Question

According to a 2011 opinion poll by Ipsos Public Affairs, 75% of American teens have a Facebbok page. It also found that 30% of girls and 24% of boys admitted to accessing their Facebook page continuoulsy throughout the day; they are termed :”super users”. The results were based on a survey of randomly selected 501 girls and 508 boys interviewed on the Ipsos U.S. Online Teen omnibus.

a.Find 95% confidence interval for the difference of proportions of super users of girls and super users of boys

b.Should we conclude that girls are more likely than boys to be super users of Facebook?

(please show work)

Explanation / Answer

Solution:

Given p1 = 0.3, p2 = 0.24 =501, n2 =508
pooled proportion:
P = n1p1+ n2p2/n1+n2 = (501)(0.3) + (508)(0.24)/501+508 = 0.2698
Given: a = 5% = 0.05
Two tailed critical value, za =1.96
(a) 95% confidence interval is
= (p1-p2) ± za sqrt[p(1-p)(1/n1+1/n2)]
= (0.3 - 0.24) ± (1.96) sqrt[(0.2698)(1-0.2698)(1/501 + 1/508)]
= 0.06 ± 0.0548
= 0.06-0.0548, 0.06 + 0.0548
= (0.0052,0.1148)
(b)Yes,
since (0.0052, 0.1148) contains only positive values

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