Question

A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts.
The following is the setup for this hypothesis test:

H0:p=0.65

Ha:p<0.65

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

Answer 1

Answer: 0.345

Step-by-step explanation:

Given: The the setup for this hypothesis test:

$H_0:p=0.65\\\\H_a:p<0.65$

Since , the alternative hypothesis is left tail , so the test is left tail test.

$P_0=0.65\\\\Q_0=1-0.65=0.35\\\\p=\dfrac{126}{200}=0.63$

The test static for population proportion is given by :-

$z=\dfrac{p-P_0}{\sqrt{\dfrac{P_0Q_0}{n}}}\\\\\Rightarrow\ z=\dfrac{0.63-0.65}{\sqrt{\dfrac{0.65-0.35}{126}}}=−0.409878030638\approx-0.4$

The p-value of z = $P(z<-0.4)= 0.3445783\approx0.345$