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Answer:
A. Ha: p < 0.3
Using the significance level for example we see that
so we have enough evidence at this significance level to FAIL to reject the null hypothesis. And on this case we can say that the proportion of employees that received the merit raise are African American is not significantly less than 0.3 or 30%.
Step-by-step explanation:
1) Data given and notation
n=60 represent the random sample taken
X=17 represent the employees that received the merit raise are African American
estimated proportion of employees that received the merit raise are African American
is the value that we want to test
represent the significance level (no given)
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
p= population proportion of employees that received the merit raise are African American
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion of employees that received the merit raise are African American is less than 0.3 or 30%. :
Null Hypothesis:
Alternative Hypothesis:
A. Ha: p < 0.3
We assume that the proportion follows a normal distribution.
This is a one tail lower test for the proportion of employees that received the merit raise are African American .
The One-Sample Proportion Test is "used to assess whether a population proportion is significantly (different,higher or less) from a hypothesized value
".
<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>
a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.
b) The sample needs to be large enough
3) Calculate the statistic
The statistic is calculated with the following formula:
On this case the value of is the value that we are testing and n = 60.
4) 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.
Based on the alternative hypothesis the p value would be given by:
Using the significance level for example we see that
so we have enough evidence at this significance level to FAIL to reject the null hypothesis. And on this case we can say that the proportion of employees that received the merit raise are African American is not significantly less than 0.3 or 30%.