A survey 1 asked a random sample of n=2752 US adults whether they had visited a

Question

A survey1 asked a random sample of n=2752 US adults whether they had visited a public library in the last 12 months. The results for males and females are shown in the table below.

1Rainie, L., “Libraries and Learning,” www.pewinternet.org/2016/04/07/libraries-and-learning/, Pew Research Center, April 7, 2016.

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A survey1 asked a random sample of n=2752 US adults whether they had visited a public library in the last 12 months. The results for males and females are shown in the table below.

Yes No Total Females 726 697 1423 Males 505 824 1329 Total 1231 1521 2752
Table 1: Have you visited a public library in the last year?

1Rainie, L., “Libraries and Learning,” www.pewinternet.org/2016/04/07/libraries-and-learning/, Pew Research Center, April 7, 2016.

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary confidence interval:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions

90% confidence interval results:

Hence,

a) p^f = 726/1423 = 0.510

p^m = 505/1329 = 0.380

p^f - p^m = 0.510 - 0.380 = 0.130

b) 90% confidence interval:

(0.10, 0.16)

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 726 1423 505 1329 0.13020479 0.01878525 0.099305801 0.16110378

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