A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least

55%

of the vote in the sample, that candidate will be forecast as the winner of the election. You select a random sample of

100

voters. Complete parts (a) through (c) below.

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Part 1

a.	What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1%?

The probability is

that a candidate will be forecast as the winner when the population percentage of her vote is

50.1%.

(Round to four decimal places as needed.)

Part 2

b.	What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 59%?

The probability is

that a candidate will be forecast as the winner when the population percentage of her vote is

59%.

(Round to four decimal places as needed.)

Part 3

c.	What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 49% (and she will actually lose the election)?

The probability is

that a candidate will be forecast as the winner when the population percentage of her vote is

49%.

(Round to four decimal places as needed.)

Part 4

d.	Suppose that the sample size was increased to 400. Repeat process (a) through (c), using this new sample size. Comment on the difference.

The probability is

that a candidate will be forecast as the winner when the population percentage of her vote is

50.1%.

(Round to four decimal places as needed.)

Part 5

The probability is

that a candidate will be forecast as the winner when the population percentage of her vote is

59%.

(Round to four decimal places as needed.)

Part 6

The probability is

that a candidate will be forecast as the winner when the population percentage of her vote is

49%.

(Round to four decimal places as needed.)

Part 7

Choose the correct answer below.

A.

Increasing the sample size by a factor of 4 decreases the standard error by a factor of 2. Changing the standard error decreases the standardized Z-value to half of its original value.

B.

Increasing the sample size by a factor of 4 decreases the standard error by a factor of 2. Changing the standard error doubles the magnitude of the standardized Z-value.

C.

Increasing the sample size by a factor of 4 increases the standard error by a factor of 2. Changing the standard error decreases the standardized Z-value to half of its original value.

D.

Increasing the sample size by a factor of 4 increases the standard error by a factor of 2. Changing the standard error doubles the magnitude of the standardized Z-value.