Question

Tom Marley and Jennifer Griggs have recently started a marketing research firm in Jacksonville, Florida. They have contacted the Florida Democratic Party with a proposal to do all political polling for the party. Since they have just started their company, the state party chairman is reluctant to sign a contract without some test of their accuracy. He has asked them to do a trial poll in a central Florida county known to have 60% registered Democratic Party voters. The poll itself had many questions. However, for the test of accuracy, only the proportion of registered Democrats was considered. Tom and Jennifer report back that from a random sample of 1000 respondents, 520 were registered Democrats.

1. Determine the probability that such a random sample would result in 520 or fewer Democrats in the sample.

2. Based on your calculations in part a, would you recommend that the Florida Democratic Party (or anyone else for that matter) contract with the Marley/Griggs marketing research firm? Explain your answer.

Answer 1

p = 0.60

n = 1000

= p = 0.6

= sqrt(p(1 - p)/n)

     = sqrt(0.6 * 0.4/1000)

     = 0.0155

= 520/1000 = 0.52

P(< 0.52)

= P(( - )/< (0.52 - )/)

= P(Z < (0.52 - 0.6)/0.0155)

= P(Z < -5.16)

= 0

Since the probability is less than 0.05, so it is unusual.

Yes, we would recommend that the Florida Democratic party contract with the Marley/Griggs marketing research firm. Because the probability of the sample proportion less than or equal to 0.52 is 0, which is less than 0.05. So a random sample of 520 or fewer Democrats is an unusual value.