Question

A publisher of a newsmagazine has found through past experience that 60% of subscribers renew their subscriptions. In a random sample of 100 subscribers, 57 indicated that they planned to renew their subscriptions. What is the p-value associated with the test that the current rate of renewals differs from the rate previously experienced? (Round your answer to four decimal places.)

Answer 1

Answer:

$z=\frac{0.57 -0.6}{\sqrt{\frac{0.6(1-0.6)}{100}}}=-0.612$  

$p_v =2*P(z$  

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

X=57 represent the subscribers indicated that they planned to renew their subscriptions

$\hat p=\frac{57}{100}=0.57$ estimated proportion of subscribers indicated that they planned to renew their subscriptions

$p_o=0.6$ is the value that we want to test

$\alpha$ 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 current rate of renewals differs from the rate previously experienced, so the system of hypothesis are:  

Null hypothesis:$p=0.6$  

Alternative hypothesis:$p \neq 0.6$  

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

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

$z=\frac{0.57 -0.6}{\sqrt{\frac{0.6(1-0.6)}{100}}}=-0.612$  

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.  

Since is a bilateral test the p value would be:  

$p_v =2*P(z$