The National Congregations Study collected data in a one-hour interview with a k

Question

The National Congregations Study collected data in a one-hour interview with a key informant-that is, a minister, priest, rabbi, or other staff person or leader. One question concerned the length of the typical sermon. For this question 390 out of 1191 congregations reported that the typical sermon lasted more than 30 minutes. Use the large-sample inference procedures to estimate the true proportion for this question with a 95% confidence interval. The respondents to this question were not asked to use a stopwatch record the lengths of a random sample of sermons at their congregations. They responded based on their impressions of the sermons. Do you think that ministers, priests, rabbis, or other staff persons or leaders might perceive sermon lengths differently from the people listening to the sermons? Discuss how your ideas would influence your interpretation of the results of this study.

Explanation / Answer

X = 390 n = 1191

95 % confidence interval

z0.025 = 1.96

p^ = X/n = 390/1191 =0.327455919

sd = sqrt(p^*q^/n) = sqrt((390/1191 )*(1-(390/1191 ))/1191)) = 0.0135981842

hence confidence interval is

(0.327455919 - 1.96* 0.0135981842 ), (0.327455919 + 1.96* 0.0135981842 )

=(0.300803, 0.3541083)

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