Question

A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is 35%. To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is determined that 156 accidents occurred in the daytime. The following is the setup for this hypothesis test: {H0:p=0.35Ha:p≠0.35 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Provide your answer below:

Answer 1

Answer: -1.78

Step-by-step explanation:

As per given description, we have

Population proportion : $p=0.35$

Sample size : n= 500

Sample proportion : $\hat{p}=\dfrac{156}{500}=0.312$

Test statistic for population proportion :-

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\=\dfrac{0.312-0.35}{\sqrt{\dfrac{0.35(1-0.35)}{500}}}\\\\=-1.78146747757\ \ \text{(Simplified)}\\\\\approx-1.78$

Hence, the test statistic for this hypothesis test for a proportion= -1.78