Question

You are testing the null hypothesis that the population proportion equals .45, using data you collected from a sample of 100 adults. You sample proportion equals .30. What does Z equal

Answer 1

Answer:

$z=\frac{0.3 -0.45}{\sqrt{\frac{0.45(1-0.45)}{100}}}=-3.015$  

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

$\hat p=0.3$ estimated proportion of interest

$p_o=0.45$ 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 true proportion is 0.45.:  

Null hypothesis:$p=0.45$  

Alternative hypothesis:$p \neq 0.45$  

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:  

$z=\frac{0.3 -0.45}{\sqrt{\frac{0.45(1-0.45)}{100}}}=-3.015$