Question

(1 point) Recent polls indicate that if a federal election would be held today, 32% 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 $n = 309$ Canadian voters, asking each Which political party will you support in the next federal election? (a) What can you expect the value of $hat{p}$ to be? (use at least two decimals in your answer) (b) Find the value of the standard deviation of $hat{p}$. Enter your answer using at least three decimals. $sigma_{hat{p}} = $ (c) Find the probability that proportion of your sample of 309 that will indicate support for the Liberal Party is at least 30% to at most 34%. Use at least four decimals in your answer. $P(0.3 le hat{p} le 0.34) = $ (d) 5% of the time, the observed value of your statistic $hat{p}$ will exceed what value? Use at least four decimals in your answer. (use four decimals in your answer)

          (1 point) Recent polls indicate that if a federal election would be held today, 32% 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 $n = 309$ Canadian voters, asking each Which political party will you support in the next federal election?
(a) What can you expect the value of $hat{p}$ to be?
(use at least two decimals in your answer)
(b) Find the value of the standard deviation of $hat{p}$. Enter your answer using at least three decimals.
$sigma_{hat{p}} = $
(c) Find the probability that proportion of your sample of 309 that will indicate support for the Liberal Party is at least 30% to at most 34%. Use at least four decimals in your answer.
$P(0.3 le hat{p} le 0.34) = $
(d) 5% of the time, the observed value of your statistic $hat{p}$ will exceed what value? Use at least four decimals in your answer.
(use four decimals in your answer)
        
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(1 point) Recent polls indicate that if a federal election would be held today, 32% 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 = 309 Canadian voters, asking each Which political party will you support in the next federal election?
(a) What can you expect the value of hatp to be?
(use at least two decimals in your answer)
(b) Find the value of the standard deviation of hatp. Enter your answer using at least three decimals.
sigmahatp =
(c) Find the probability that proportion of your sample of 309 that will indicate support for the Liberal Party is at least 30% to at most 34%. Use at least four decimals in your answer.
P(0.3 le hatp le 0.34) =
(d) 5% of the time, the observed value of your statistic $hat{p}$ will exceed what value? Use at least four decimals in your answer.
(use four decimals in your answer)

Added by Carrie Z.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Transcript

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00:01 For this problem, for part a, we would have that we would expect our p hat value, or the average of the p hat values, to be equal to the population proportion, which we're told is equal to 0 .32.
00:14 For part b, we'd have that the standard deviation of our sample proportions is going to be equal to the square root of our population proportion times one minus the population proportion divided by our sample size.
00:29 In this case, that's the square root of 0 .32 times 1 minus 0 .32 divided by n is 309.
00:44 And so we should find that the standard deviation of the sample proportions is equal to roughly 0 .0265.
00:53 Then for part c to find the probability of p hat being between 0 .3 and 0 .3, let me double check the calculation there.
01:07 Pardon me, 0 .3 and 0 .34.
01:10 What we can do is find the probability of p hat being between the different corresponding z scores, where the z score is going to be given by, for instance, for the z score of 0 .3, that would be, be given by 0 .3 minus 0 .32 divided by our standard deviation, 0 .0265, which would give a result of negative 0 .7547.
01:41 And we'd have that 0 .34.
01:44 It's the same amount or same distance above the mean value.
01:48 So we would have that the corresponding z scores would be 0 .7 or negative 0 .7547 for the lower bound and positive 0 .7547 for the upper bound...
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