Respuesta :
Answer:
The value of the test statistics is 1.85.
Step-by-step explanation:
We are given that a political study took a sample of 900 voters in the town and found that 62% 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 59%.
Let p = percentage of residents who favor construction.
SO, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 59% {means that the percentage of residents who favor construction is below or equal to 59%}
Alternate Hypothesis, [tex]H_A[/tex] : p > 59% {means that the percentage of residents who favor construction is above 59%}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = percentage of residents who favor construction in a sample of 900 voters = 62%
n = sample of voters = 900
So, test statistics = [tex]\frac{0.62-0.59}{{\sqrt{\frac{0.62(1-0.62)}{900} } } } }[/tex]
= 1.85
The value of the test statistics is 1.85.
