In a study to estimate the proportion of residents in a certain city and its sub

Question

In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a natural gas-fired power plant (in the suburbs), it is found that 63 of 100 urban residents favor the construction while only 59 of 125 suburban residents are in favor. Is there a significant difference between the proportions of urban and suburban residents who favor the project? In addition to conducting the z-test, conduct a two-sided test of the odds ratio: Ho : theta = 1 where

Explanation / Answer

1.      FindORhat and test for association.

Favor

Against

Urban

63

37

100

Suburbs

59

66

125

122

103

225

1.904718

log(OR hat)

0.279831

Var[log(OR hat)]

0.075001

SD[log(OR hat)]

0.273863

z

1.021793

P(|Z| > z)

0.306879

Step 1: State the null andalternative.

H0: OR = 1

H1: OR 1

Step 2: Find the criticalstatistic.

At = 0.05, z1-/2 =1.96.

Critical z region is: (-, -1.96) or (1.96,)

Step 3a: Standard error

SE[log(ORhat)] = (1/a + 1/b +1/c + 1/d)

   = 0.273863

Step 3b: Test statistic

z = [log(ORhat) – 0] /SE[log(ORhat)]

    = 0.279831 / 0.273863=1.02

Step 3c: p-value

p-value = P(|Z| > 1.02) = 0.307

Step 4: Conclusion.

Favor

Against

Urban

63

37

100

Suburbs

59

66

125

122

103

225

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