Myers used a random sample of 375 married couples and foundthat 132 had three pr

Question

Myers used a random sample of 375 married couples and foundthat 132 had three preferences in common. another random sample of571 couples showed that 217 had two personality preferences incommon. let p1 be the population proportion of all married coupleswho have three personality preferences in common. let p2 be thepopulation proportion of all married couples who have twopersonality preferences in common. a.) find a 90% (1.645) confidence interval for p1-p2 b.) examine the confidence interval in part a and explain whatit means in the context of this problem. does the confidenceinterval contain all positive, all negative, or both positve andnegatives? what does this tell you about the proportion of marriedcouples with three personality preferences in common compared withthe proportion of couples with two preferences in common (at the90% confidence level)? Myers used a random sample of 375 married couples and foundthat 132 had three preferences in common. another random sample of571 couples showed that 217 had two personality preferences incommon. let p1 be the population proportion of all married coupleswho have three personality preferences in common. let p2 be thepopulation proportion of all married couples who have twopersonality preferences in common. a.) find a 90% (1.645) confidence interval for p1-p2 b.) examine the confidence interval in part a and explain whatit means in the context of this problem. does the confidenceinterval contain all positive, all negative, or both positve andnegatives? what does this tell you about the proportion of marriedcouples with three personality preferences in common compared withthe proportion of couples with two preferences in common (at the90% confidence level)?

Explanation / Answer

Given n1=375, p1=132/375 = 0.35           n2=571,p2=217/571 =0.38 =0.1, Z(0.05)=1.645 (check normal table) The 90% CI is (p1 - p2) ± Z*(p1*(1-p1)/n1 +p2*(1-p2)/n2) --> (0.35-0.38) ± 1.645*sqrt(0.35*(1-0.35)/375 +0.38*(1-0.38)/571) --> ( -0.0825, 0.0225)

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