An article a Florida newspaper reported on the topics that teenagers most want t

Question

An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 546 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 95% confidence level. Express the answer in the form P plusminus E and round to the nearest thousandth. A) 0.37 plusminus 0.040 B) 0.37 plusminus 0.002 C) 0.63 plusminus 0.040 D) 0.63 plusminus 0.002.

Explanation / Answer

Solution:

n=546

The proportion of teenagers wanting more discussion about school = 37%

p = 0.37

1 - p = 0.63

Given a=0.05, Z(0.025) =1.96 (from standard normal table)

So 95% confidence interval is

p+/-Z*sqrt(p*(1-p)/n)

--> 0.37+/- 1.96*sqrt(0.37*(1-0.37)/546)

--> 0.37 +/- 0.0404

Option A) is correct.

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