A survey35 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 Table 6.5. Have you visited a public library in the last year? Yes No Total Females 726 697 1423 Males 505 824 1329 Total 1231 1521 2752 (a) Find p^f and p^m, the sample proportions who have visited a public library in the last 12 months, for females and males respectively. What is the difference in sample proportions p^f−p^m? (b) Find a 95% confidence interval for the difference in population proportions pf − pm. (c) Can we conclude from the confidence interval that there is a difference in proportions? If so, are males or females more likely to visit the public library?
Example 3. Public Libraries and Gender
A survey35 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 Table 6.5.
|
Have you visited a public library in the last year? |
|||
|
|
Yes |
No |
Total |
|
Females |
726 |
697 |
1423 |
|
Males |
505 |
824 |
1329 |
|
Total |
1231 |
1521 |
2752 |
(a) Find p^f and p^m, the sample proportions who have visited a public library in the last 12 months, for females and males respectively. What is the difference in sample proportions p^f−p^m?
(b) Find a 95% confidence interval for the difference in population proportions pf − pm.
(c) Can we conclude from the confidence interval that there is a difference in proportions? If so, are males or females more likely to visit the public library?
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FIND 90% CONFIDENCE INTERVAL FOR THE DIFFERENCE IN POPULATION PROPORTIONS Pf -Pm .
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