Posted by daniel on Wednesday, April 20, 2011 at 12:03am.
suppose you are testing Ho:p=.65 versus Ha: p<.65 . for a random sample of 100 people, x=58, where x denotes the number in the sample that have the characteristic of interest . use a .01 level of significance to test this hypothesis.

statistics  MathGuru, Wednesday, April 20, 2011 at 8:05pm
Null hypothesis:
Ho: p = .65 >meaning: population proportion is equal to .65
Alternative hypothesis:
Ha: p < .65 >meaning: population proportion is less than .65
Using a formula for a binomial proportion onesample ztest with your data included, we have:
z = (.58  .65) >test value (58/100 = .58) minus population value (.65)
divided by
√[(.65)(.35)/100] > .35 represents 1  .65 and 100 is the sample size.
Use a ztable to find the critical or cutoff value for a onetailed test (lower tail) at .01 level of significance. The test is onetailed because the alternative hypothesis is showing a specific direction (less than).
If the test statistic exceeds the critical value you find from the table, reject the null. If the test statistic does not exceed the critical value from the table, do not reject the null.
You can draw your conclusions from there.
I hope this will help get you started.
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