Statistics - Hypothesis testing question

[Nephilim]

Hello folks. This was in my exam and I wasn't sure how to solve it.

Homework Statement

A sample of 67 respondents was taken collectively by a population of 6,456 units. The number of those who said they were available to implement a development program were 35. To implement the program requires the agreement of at least 60% of the population. With a significance level of 5% you can believe that this program will be implemented or is more likely to be rejected?

Homework Equations

Given this table:
http://imageshack.us/f/191/unled1lx.jpg/

The Attempt at a Solution

Should I find the p value here, since we have percentage? If so then we'd have the null hypothesis : p<0.6 and the alternative hypothesis : p>=0.6 and the rest is easy, finding the Z value and looking it up. But I have a problem identifying what type of test is needed.
Also, what differs if the sample is taken WITH or WITHOUT remission?


Thank you in advance.

 

[lippyka]

In this case, you would use a two-tailed test of proportions to determine if the program will be implemented or rejected. The null hypothesis would be that the population proportion of those available to implement the program is less than or equal to 0.6, and the alternative hypothesis would be that the population proportion is greater than 0.6. To find the p-value, you would calculate the observed proportion from the sample (35/67 = 0.52) and then compare it to the critical value of 0.6. With a significance level of 5%, the p-value would need to be less than 0.05 in order to reject the null hypothesis and conclude that the program is more likely to be implemented. Whether the sample is taken with or without remission does not affect the type of test used, but it may affect the results. If the sample is taken with remission, then more people may be available to implement the program, which would increase the observed proportion and make it more likely that the null hypothesis would be rejected.