00:01
So our question says that suppose that you want to run a hypothesis test on the population proportion.
00:05
You have a sample of 300 observations and a sample proportion is 0 .63.
00:09
Provide the following.
00:11
So we have to set up a 2 -tier hypothesis test to test whether the population proportion is equal to 0 .70.
00:16
Use a 5 % level of significance as 0 .05.
00:20
So you state your null hypothesis, you state the alternative hypothesis.
00:24
You determine the test statistics, determine the p -value, determine the critical values for the hypothesis are, and clearly explain whether you should reject or not reject in all hypothesis at a 5 % level of significance.
00:37
According to our question, we have our sample size n which is equals to 300.
00:42
We have the sample proportion p cap.
00:45
We have that to be caused to 0 .63.
00:48
We have the population proportion p.
00:51
We actually have that to be equal to 0 .70.
00:54
So the first step is first to state the null and alternative hypothesis.
00:57
Our h notice based on the fact that p is equals to 0 .70 and the alternative hypothesis is that p is not equals to 0 .70 so that being said we need to get our test statistics test statistics can either be a z test or et test and there is actually a rule that allows us to use a normal distribution to model sample proportion question and that rule says that n -p cap must be greater than no equals to 5 and nq cap must also be greater than a cross to 5 once we can satisfy these two conditions we can be able to use a normal distribution to approximate our data set so let's try that 300 times 0 .63 when we do the match with our calculator 300 times 0 .63 that gives us 189 so pick up is going to be 1 minus 0 .63 and that gives us 0 .3 so 300 times 0 .37 that gives us 111 so 300 times 0 .37 that gives us one one one as you can see both values are greater than 5 so that simply implies that our test statistics is going to be a z test so we have z equals to pick up minus p divided by the square root of p times q divided by n uh pickup in this case of ars is going to be 0 .63 minus 0 .70 divided by the square root of 0 .70 times 0 .30 divided by 300.
02:36
So that's a minus 0 .07 divided by using our calculator, 0 .70 times 0 .30 divided by 300 and that gives us 0 .0665.
02:51
So our z equals to minus 0 .07 divided by 0 .0265.
02:58
That gives us minus minus 2 .65...