SOLUTION: I need some help with some statistics problems. I'll start with the one below. If possible a simple explanation for each of the answers below would be appreciated. What formula to

Question 900557: I need some help with some statistics problems. I'll start with the one below. If possible a simple explanation for each of the answers below would be appreciated. What formula to use and where the numbers came from to fill in the formula? I believe the null hypothesis is p>=.76 and the alternative is p<.76, but am not sure and may be completely off. I'm guessing I use the formula z=xbar-mu0/sigma/sqrt(n), but I'm not quite sure on that either and I'm not sure where to get the numbers??? Thanks in advance.
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 76%. In a random sample of 250 married couples who completed her program, 187 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 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:
The value of the test statistic (round to at least 3 decimal places):
The critical value at the 0.05 level of significance (round to at least 3 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 76%?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 76%. In a random sample of 250 married couples who completed her program, 187 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 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: p >= 0.76 (claim)
The alternative hypothesis: H1: p < 0.76
------------------------------------------------
The type of test statistic: z-value
--------------------------------------
Note: p-hat = 187/250 = 0.748
----------------------------------------
The value of the test statistic (round to at least 3 decimal places):
z(0.748) = (0.748-0.76)/sqrt(0.76*0.24/250) = -0.4443
----------------------------------------------
The critical value at the 0.05 level of significance (round to at least 3 decimal places): invNorm(0.05) = -1.645
-----------
Can we reject the psychologist's claim that the proportion of married couples for whom her program can prevent divorce is at least 76%?
Since the test statistic is not in the reject interval, fail to reject Ho.
The test results support the claim.
--------------
Cheers,
Stan H.
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