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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.

Respuesta :

JeanaShupp

Answer: 0.345

Step-by-step explanation:

Given: The the setup for this hypothesis test:

[tex]H_0:p=0.65\\\\H_a:p<0.65[/tex]

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

[tex]P_0=0.65\\\\Q_0=1-0.65=0.35\\\\p=\dfrac{126}{200}=0.63[/tex]

The test static for population proportion is given by :-

[tex]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[/tex]

The p-value of z = [tex]P(z<-0.4)= 0.3445783\approx0.345[/tex]

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