00:01
For this question, we have these null hypotheses.
00:05
The null hypothesis is that the population proportion is 0 .26, and the alternative hypothesis is that it is not .26.
00:15
And we want to test these hypotheses at a significance level of 5%.
00:22
To perform this test, we have a sample of size 809, which yielded a sample proportion of 0 .24.
00:30
The first question we are asked is what are the critical values of z for this test? looking at the alternative hypothesis, it's a not equal as hypothesis, which means that this is a two -tailed test, so there are two critical values, and they are given by plus or minus z sub alpha over 2.
00:54
And for this test, alpha is 0 .05, so this is plus or minus z sub 0 .025, which means that our critical values are plus or minus 1 .96.
01:18
The second question is what is the value of the test statistic? now for this situation, our test statistic follows the standard normal distribution, and it's given by this formula, the sample proportion minus the null hypothesized proportion divided by the square root of the null hypothesized proportion times 1 minus this proportion over the sample size.
01:52
So this gives us the following.
02:14
And this comes out to minus 1 .30 approximately.
02:20
Rounded to three decimal places, this is going to be minus 1 .297...