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 80%. In a random sample of 245 married couples who completed her program, 183 of them stayed together. Based on this sample, can we reject the psychologist's claim at the 0.1 level of significance? Perform a one-tailed 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 The null hypothesis: р H . 0 X S The alternative hypothesis: A O=O OSO DO The type of test statistic: (Choose one) DO O<O O> The value of the test statistic: (Round to at least three decimal places.) X 5 ? The critical value at the 0.1 level of significance: (Round to at least three decimal places.) Can we reject the psychologist's claim that the proportion of married couples for whom her program can prevent divorce is at least 80%? Yes No

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.8
Alternative Hypothesis, Ha: p < 0.8

single proportion z test

Rejection Region
This is left tailed test, for α = 0.1
Critical value of z is -1.28.
Hence reject H0 if z < -1.28

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.7469 - 0.8)/sqrt(0.8*(1-0.8)/245)
z = -2.078

Rejection Region
This is left tailed test, for α = 0.1
Critical value of z is -1.282.
Hence reject H0 if z < -1.282

Yes, we can reject the claim