Question

A publisher reports that 45% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 370 found that 40% of the readers owned a laptop. determine the p-value of the test statistic

Answer 1

Answer:

$z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933$  

$p_v =2*P(z<-1.933)=0.0532$  

Step-by-step explanation:

Information given

n=370 represent the sample selected

$\hat p=0.4$ estimated proportion of  readers owned a laptop

$p_o=0.45$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Creating the hypothesis

We need to conduct a hypothesis in order to test if the true proportion of readers owned a laptop is different from 0.45, the system of hypothesis are:  

Null hypothesis:$p=0.45$  

Alternative hypothesis:$p \neq 0.45$  

The statistic is:

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

Replacing we got:

$z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933$  

Calculating the p value  

We have a bilateral test so then the p value would be:

$p_v =2*P(z<-1.933)=0.0532$