(1 point) Recent polls indicate that if a federal election...

(1 point) Recent polls indicate that if a federal election would be held today, 32.1% of Canadian voters would cast his/her vote for the Liberal Party candidate in his/her riding. Suppose you are a political pollster, and you are to randomly pick n = 334 Canadian voters, asking each Which political party will you support in the next federal election? (a) What can you expect the value of p? to be? Enter your answer using all the decimals you can. (b) Find the value of the standard deviation of p?. Enter your answer using all the decimals you can. ?_p? = (c) Find the probability that proportion of your sample of 334 that will indicate support for the Liberal Party is at least 29% to at most 36%. Enter your answer using all the decimals you can. P(0.29 ? p? ? 0.36) = (d) 4% of the time, the observed value of your statistic p? will exceed what value? Enter your answer using all the decimals you can.

Transcript

00:01 Item a, the expected value of b had here, so it's the same as saying what is the expectation of this, by definition, is the proportion in the population, which is given by the question as being the 32 .1%.

00:18 So we should write this as a proportion.

00:21 So this will be the answer for item a.

00:24 For item b, we have to compute the steady deviation, or the p hat.

00:32 So here we're going to use the formula again.

00:35 So this is given by the square root of p, 1 minus p divided by n.

00:41 So in our case p is 0 .31 times 1 minus 0 .321 divided by the total number of in this case voltre selected which is 3 3 4.

00:57 So this here will be 0 .6.

01:00 0, 25, 5, and 5.

01:07 So now in item c, we should compute what is the probability that p hat will be between these two numbers here.

01:16 So to do this, we're gonna use the information in a and b.

01:21 And another thing that we can use is that we can compute this probability using the normal distribution.

01:30 So the idea here is we are considering that p hat has a normal distribution with mean equals to the p and the standard deviation includes to what we compute in b.

01:46 So this square root.

01:49 So as you can see, item a we computed the mean of the distribution and in item b, the standard deviation of the distribution.

01:57 The only thing that was missing is that we can say that this is a normal distribution.

02:04 So to compute this, we should consider that p -hat has a normal distribution.

02:08 And another thing that we can use here is the z -score approach.

02:13 Now that p -hat has a normal distribution, we can compute this using the z -score approach, which basically means that instead of like just considering the distribution of p -hat, will be easier to compute this using the standard normal distribution, because for the standard normal distribution, we have tables that provides the area under a specific value in the distribution, so we can use that to compute this probability.

02:43 So to do this, we should, from each value that we have here, we should subtract the mean of the p -hater distribution, so from item 8, this is 0 .32 .1, and divide this difference by the square root, or in this case, the standard deviation.

02:59 So basically, this would be 0 .0 -2555 from the previous item...

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