6.147 – Public Libraries and Children 1. Compute the 90% confidence interval (sh
ID: 3065018 • Letter: 6
Question
6.147 – Public Libraries and Children
1. Compute the 90% confidence interval (show your work; note that no software is needed, just a calculator):
2. Interpret the confidence interval:
3. Is it plausible there is a significant difference? Explain.
that there is a difference in proportions? If so, are males or females more likely to visit the pub- lic library? 6.147 Public Libraries and Children Exercise 6.146 ntroduces a survey that asked a random sample of n 2752 US adults whether they had visited a public library in the last 12 months. We see in that data that more females than males visit the library, but there is likely a confounding variable. Table 6.6 shows the survey results broken down by whether or not the participant is a parent of a minor. Find and interpret a 90% confidence interval for pc PN the difference in proportion visiting the library between those with children in the house and those without. Table 6.6 Have you visited a public library in the last year? Children in house No children in house Total Yes 421 810 1231 No 411 1110 1521 Total 832 1920 2752 6.148 Metal Tags on Penguins and Survival Data 1.3 on page 10 discusses a study designed to test
Explanation / Answer
1) p1 = 421/ 832 = 0.506, 1 - p1 = 0.494, n1 = 832,
p2 = 810/ 1920 = 0.422, 1 - p2 = 0.578, n2 = 1920,
Alpha = 0.1
The Zcritical (2 tail) for Alpha = 0.1, is 1.645
The Confidence Interval is given by (p1- p2)± ME, where
(p1- p2) = 0.506-0.422 = 0.084
ME = Z critical*sqrt[p1(1-p1)}/n1+p2(1-p2)/{n2}] = 1.96* sqrt[{0.506*0.494}/{832} + {0.422*0.578}/{1920}] = 0.034
The Lower Limit = 0.084 - 0.034 = 0.050
The Upper Limit = 0.084 + 0.034 = 0.118
The Confidence Interval is (0.050 , 0.118)
2) We are 90% confident that the true difference in proportions of the population of people who go to the library when they have or dont have children at home is within the limits of 0.050 and 0.118.
3) Yes, there is a significant difference as the interval does not contain 0, which eliminates the possibility of p1 = p2
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