The University of Wisconsin employs 200 teaching assistants (TAs). If one-third

Question

The University of Wisconsin employs 200 teaching assistants (TAs). If one-third of the TAs sign a petition calling for a collective bargaining election, an election will be held.

(a) A survey of 25 TAs indicates that 40% will sign the petition. What is the probability that a sample such as this could have occurred if one-third or fewer of the TAs in the population will sign such a petition?

(b) The university surveys 25 additional TAs, so they now have a survey of 50 TAs, which also indicates that 40% will sign the petition. What is the probability that a sample such as this could have occurred if one-third or fewer of the TAs in the population will sign such a petition?

Explanation / Answer

Since the sample that we are drawing from is a finite number = 200, we use a hyper geometric distirbution

We find the Z-value to approximate the given distribution in normal terms

Thus,

n = 25, N = 200, p = 1/3

Thus, mean = np = 25/3

SD = sqrt [ (200 - 25) * (25 * 1/3) * (2/3) / 199]

= 2.21

Thus,

z = 10 - 8.3333 / 2.21

= 0.7540

Thus, P(Z < 0.7540) = 0.7745

P ( Z > 0.7540) = 0.2254

b)

Similarly,

n = 50, N = 200, p = 1/3

Thus, mean = np = 50/3

SD = sqrt [ (200 - 50) * (50 * 1/3) * (2/3) / 199]

= 2.894

Thus,

z = 20 - 16.666 / 2.894

= 1.1518

Thus, P(Z < 1.1518) = 0.8753

P ( Z > 1.1518) = 0.1247

Hope this helps.

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