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Test of hypothesis: difference between proportions

A survey was completed to estimate the proportion of residents in support of constructing a new football stadium, at tax payer expense, to accommodate an NFL team in the LA area. It was found that 71 of 100 LA city residents favored the construction while 78 of 135 residents in the rest of the county were in support. Determine if there is a significant difference between the proportion of city and the other county residents in support of the stadium construction. State your hypotheses and use a P-value in your argument.

Solution Preview

Null Hypothesis: H0: p1=p2 or p1-p2=0

(There is no difference between proportion of of residents in LA and the rest of the country in support of the stadium)

Alternative Hypothesis: H1: p1>p2

(Proportion of of residents in LA in support of the stadium is greater than the proportion of residents in rest of the country in support of the stadium)

Since the significance level for testing this hypothesis has not been mentioned

we will assume a (alpha) = 0.05 or 5.00%

p1,p2= proportions of residents in support of stadium in LA and the rest of the country respectively

n1,n2= sample sizes

We will carry out a one tailed test for differences between proportions

(since we are testing p1>p2 ; if we were testing p1not equal to p2 , it would have been a two tailed ...

Solution Summary

Hypothesis that there is a significant difference between the proportion of city and the other county residents in support of the stadium construction is tested.

$2.19