thank you so much for help, it helped a lot..

Question

But is it ok to find p value from a calculator?

Answer 1

This is going to be a left-tailed test and it Is a proportion. Your null hypothesis is H_o: p ≥ 25%, and the alternative hypothesis is H_A: p<25%.

n=998

Phat(sample proportion)=.173

P(Population proportion)=.25

α=.05

It is a left-tailed test. 1.0-.05=.9500

Using a Z-table, we use the probability of .9500 to find the correct Z-score, which is -1.645. So, if we get a test statistic that is less than -1.645, we will reject the Null Hypothesis.

We now standardize the normal random variable using the following standardized form. This will be the test statistic.

Z= (Phat - P) ⁄ √P(1-P) ⁄ n

Z= (.173 - .25)/√.25(.75) ⁄ 998

Z= -5.62

-5.62 is less than -1.645, so we reject the null hypothesis.

P-Value is the smallest αlpha at which H₀ can be rejected. Another words, it is the area under the normal curve from the test statistic through the tail that represents the alternative hypothesis (H_A). Our test statistic is -5.62. It may be difficult to estimate the probability relevant to this Z-score. Instead, we can approach it differently.

For P-Value, we use the following decision criteria.

We reject the null hypothesis when the P-Value is less than α. If P-Value is greater than alpha, then the test statistic will not lie within the rejection region. Our alpha is .05 at the critical value of -1.645. Our test statistic is -5.62, making the P-Value very small. It is impossible for the area to be more than .05, so we can reject the null hypothesis.

Answer 2

If we are testing the claim that at least 25% disagree with that statement (a right-tailed test) and the random sample has less than 25% (17.3%) disagreeing, then there really is no need to perform a statistical test to determine that the claim is rejected.