Most married couples have two or three personality preferences in common. A rand
ID: 3177702 • Letter: M
Question
Most married couples have two or three personality preferences in common. A random sample of 380 married couples found that 134 had three preferences in common. Another random sample of 552couples showed that 224 had two personality preferences in common. Let p1 be the population proportion of all married couples who have three personality preferences in common. Let p2 be the population proportion of all married couples who have two personality preferences in common.
(1) Find a 99% confidence interval for p1 – p2. (Use 3 decimal places.)
a) find the Lower limit:
b) find the Upper limit:
Explanation / Answer
The statistical software output for this problem is:
Two sample proportion confidence interval:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
99% confidence interval results:
0.029805201
Hence,
99% confidence interval for p1 - p2 will be:
(-0.136, 0.030)
Lower Limit: -0.136
Upper Limit: 0.030
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 134 380 224 552 -0.053165523 0.032211266 -0.136136250.029805201
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