Question

A publisher reports that 53%53% 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 250250 found that 44%44% 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

`z=\frac{0.44 -0.53}{\sqrt{(0.53(1-0.53))/(250)}}=-2.85`

`p_v =2*P(z<-2.85)=0.0044`

Explanation:

Data given and notation

n=250 represent the random sample taken

`\hat p=0.44` estimated proportion of of the readers owned a particular make of car.

`p_o=0.53` is the value that we want to test

`\alpha=0.05` represent the significance level

z would represent the statistic (variable of interest)

`p_v` represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true porportion is equal to 0.53.:

Null hypothesis:
`p=0.53`

Alternative hypothesis:
`p \\eq 0.53`

When we conduct a proportion test we need to use the z statistic, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion
`\hat p` is significantly different from a hypothesized value
`p_o`.

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

`z=\frac{0.44 -0.53}{\sqrt{(0.53(1-0.53))/(250)}}=-2.85`

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

`p_v =2*P(z<-2.85)=0.0044`