Many teens have posted profiles on a social-networking website. A sample survey

Question

Many teens have posted profiles on a social-networking website. A sample survey in 2007 asked a random sample of teens with online profiles if they included false information in their profiles. Of 170 younger teens (aged 12 to 14), 117 said “yes.” Of 317 older teens (aged 15 to 17), 152 said “yes.”

Do these samples satisfy the guidelines for the large-sample confidence interval?

a. No, because the sample sizes differ too much. b. Yes, because the samples are larger than 40. c. Yes, because the sample size is more than 5 in each group. d. Yes, because the numbers of successes and failures are more than 10 in both samples.

Give a 95% large sample confidence interval for the difference between the proportions of younger and older teens who include false information in their online profiles.

a. 0.4598 to 0.6450
b. 0.1200 to 0.2974
c. 0.1180 to 0.2948
d. 0.1342 to 0.2832

Explanation / Answer

a) d. Yes, because the numbers of successes and failures are more than 10 in both samples.

b) Standard error, SEp1-p2 = sqrt{ [p1 * (1 - p1) / n1] + [p2 * (1 - p2) / n2] } = 0.0452712

For 0.05 significance, zcrit = 1.96

95% CI = p1 - p2 +/- zcrit * SE = 0.6882-0.4795 +/- 1.96*0.0452712 = (0.1200, 0.2974) Option b

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