00:01
A congressional candidate who currently has the support of only 44 % of the voters run a television spot that aggressively attacks the character of his opponent.
00:09
So to determine whether the advertisement changes his support level, his poll list as surveys a simple random sample of 450 voters and find that 186 supports the candidate.
00:20
This procedure, this produces a 95 % confidence in town for the proportion of voters who support him.
00:27
So we have the 95 % confidence is about to be between 0 .368 and 0 .459.
00:35
Suppose, so the first question says, suppose it's police start conduct a test of h -notice that p is equal to 0 .44 versus the alternative that p is not equal to 0 .44.
00:46
So using a 5 % level of significance, use the confidence interval to determine whether to reject or accept or feel to reject the null hypothesis, which should explain the reason and also find the p value for the test describing party and explain what it means in the context of the problem so basically we have a population proportion p to be equals to 44 percent we have our sample size n we have it to be close to 450 and out of this 450 we have our x to be equals to 186 so our sample proportion pick up is our 186 divided by 450 1 .86 divided by 450 that gives us 0 .41.
01:40
So the question says that we have our confidence intervals will be between 0 .368 and 0 .459.
01:47
So 95 % confidence interval is actually 0 .368 and 0 .459.
01:58
We also have the non -hypotesis h0 to be based on the fact that p is equal to 0 .44 and the alternative hypothesis is that p is not across 0 .44 now we can use our confidence interval to make decision when it comes to hypothesis test and so this is like a a melting pot for confidence interval and hypothesis test and the condition or the decision rule is based on the fact that if the population proportion is actually a member of the confidence interval then you actually fail to reject the null hypothesis and if the population proportion is not a member of the confidence interval you reject the null hypothesis our population proportion in this because of as p is equals to 0 .44 so let's check our interval to see whether 0 .44 is actually a member of this confidence interval and as we can see 0 .44 is actually a member of the confidence interval that we uh that was given to us so that means we fail to reject the null hypothesis so the next question which is question b so we call this so our decision is that we fail to reject the null hypothesis so this is our question a so question b says that i find the p value for the test and describe it in part yeah excuse me find a p value for test for the test describing part a and explain what is measures in the context of the those problem so to get our p value we we need to get our test statistics and our test statistics is definitely going to be a z test because we have a very large sample size it obeys the central limit term so we have that z is equals to pick up minus p divided by the square root of p times q divided by n so our pickup is 0 .41 minus 0 .44 divided by the square root of so 0 .44 times 0 .56 divided by 450 so z is equals to so 0 .41 minus 0 .4 for das is minus 0 .03 divided by the square root of 0 .4 times 0 .56 divided by 450 dash 0 .0 2 3 4 so when we do the math minus 0 .03 divided by 0 .023 and that is minus 1 .28...