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 onetailed 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.

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
PValue =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%
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