A Gallup poll surveyed a random sample of 407 US teenagers. One question they we

Question

A Gallup poll surveyed a random sample of 407 US teenagers. One question they were asked was, "How strict are your parents compared to most of your friends' parents?" The answer choices given were "more strict", "less strict" and "about the same". The choice "more struct" was selected by 127 of the respondents.

What is the sample proportion of respondents who answered "more strict"? [answer to 3 decimal places - answer as a fraction, not as a percentage]

What is the standard error of the sample proportion of respondents who answered "more strict"? i.e. s.e.(p^) [answer to 4 decimal places]

Suppose p denotes the population proportion of respondents who believe their parents are "more strict" than their friends' parents. Which of the following options gives the formula for conservative interval estimate for p?
p^?1127????
p^?1407????
p^?s.e.(p^)127????
p^?s.e.(p^)407????

Which of the formulas below gives the 95% confidence interval for p?
p^?1.645×s.e.(p^)
p^?2.576×s.e.(p^)
p^?1.96×s.e.(p^)
p^?2.326×s.e.(p^)

A: 0.073 B: 0.256 C: 0.285 D: 0.312 E: 0.357 F: 0.981

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:

Hence,

Sample proportion = 0.312

OPtion D is correct.

Standard error = 0.0230

Option A is correct.

95% confidence interval for p: Option C is correct.

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 127 407 0.31203931 0.022966206 0.26702637 0.35705225

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