Question

A psychologist specializing in marriage counseling claims that, among all married couples, the proportion p for whom her communication program can prevent divorce is at least 78%. In a random sample of 245 married couples who completed her program, 173 of them stayed together. Based on this sample, can we reject the psychologist's claim at the 0.05 level of significance? Perform a one-talled test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. a р The null hypothesis: x S The alternative hypothesis: B 020 The type of test statistics Choose one) DO The value of the test statistici Round to at least three decimal places.) X 5 The p-values Round to at least three dedim. Can were the schodam that the proportion of married couples for whom her Conte

Answer 1

1)

null Hypothesis:              Ho:   p ≥		0.780
alternate Hypothesis:    Ha: p <		0.780

2_)

type of test statistic =z

3)

sample success x   =		173
sample size          n    =		245
std error σp =√(p*(1-p)/n) =		0.0265
sample prop p̂ = x/n=173/245=		0.7061
z =(p̂-p)/σp=(0.706-0.78)/0.026=		-2.791

p value =0.0026

Yes (since p value <0.05)