Question

The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 1300 voters in the town and found that 66% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is not equal to 69%. Testing at the 0.05 level, is there enough evidence to support the strategist's claim?

Step 4 of 7:

Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.69

Ha : p 0.69

= 0.66

P0 = 0.69

1 - P0 = 1 - 0.69 = 0.31

Test statistic = z =

= - P0 / [P0 * (1 - P0 ) / n]

= 0.66 - 0.69 / [(0.69 * 0.31) / 1300 ]

Test statistic = z = -2.34

P(z < -2.34) = 0.0096

P-value = 2 * 0.0096

P-value = 0.0192

= 0.05    

P-value <

Reject the null hypothesis .

There is sufficient evidence to support the strategist's claim