Question

INCLUDE DEGREE OF FREEDOM IF ANYTHING OTHER THAN Z.

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

77%

. In a random sample of

225

married couples who completed her program,

168

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.

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF
The value of the test statistic: (Round to at least three decimal places.)
The p-value: (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 77% ?		Yes	No

Answer 1

we have to test the claim of psychologist that among all married couples the proportion p for whom her communication program can prevent divorce is at least 77%

Hence

Null hypothesis : p>0.77

Alternative Hypothesis : p<0.77

Since we are testing proportions so we will use 1 sample Z test for proportions

now we have sample size=n=225

no.of couples stayed together after the course =x=168

so sample proportion is given by

Now test statistics is given by

since test is left tailed so

P-Value =P(Z<-0.820)=0.206

since P value is more than level of significance (0.01) hence we failed to reject H0 Hence we do not have enough evidence to reject Her claim hence

we can not reject the psychologist's claim that the proportion of married couples for whom her program can prevent divorce is at least 77%