Most married couples have two or three personality preferences in common. A rand

Question

Most married couples have two or three personality preferences in common. A random sample of 372 married couples found that 132 had three preferences in common. Another random sample of 562couples showed that 204 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.

(a) Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)

lower limit upper limit

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

95% confidence interval results:

Hence,

95% confidence interval will be:

Lower limit = -0.071

Upper limit = 0.055

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 132 372 204 562 -0.0081506142 0.032044286 -0.07095626 0.054655032

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