A political study took a sample of 1000 voters in the town and found that 39% 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 above 35%. Find the value of the test statistic. Round your answer to two decimal places.
Solution:
Given ,
n = 1000
Let be the sample proportion.
= 39% = 0.39
Let p be the population proportion.
Claim to be tested is " p is above 35% " i.e. " p > 0.35 "
Null and alternative hypothesis are
H0 : p = 0.35
H1 : p > 0.39
The test statistic z is
z =
= (0.39 - 0.35)/[0.35*(1 - 0.35)/1000]
= 2.65
The value of the test statistic is z = 2.65
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