Question

A publisher reports that 31% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 100 found that 21% of the readers owned a particular make of car. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Answer:

$z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162$  

Since is a bilateral test the p value would be:  

$p_v =2*P(z<-2.162)=0.0306$  

Step-by-step explanation:

Information given

n=100 represent the random sample taken

$\hat p=0.21$ estimated proportion of the readers owned a particular make of car

$p_o=0.31$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We need to conduct a hypothesis in order to test if the true proportion is 0.31 or no.:  

Null hypothesis:$p=0.31$  

Alternative hypothesis:$p \neq 0.31$  

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

And replacing we got:

$z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162$  

Since is a bilateral test the p value would be:  

$p_v =2*P(z<-2.162)=0.0306$