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Answer:
If we compare the p value and the significance level given we have
so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 8% of significance the true proportion of defectives is different from 0.05.
Step-by-step explanation:
1) Data given and notation n
n=300 represent the random sample taken
X=13 represent the defectives
estimated proportion of defectives
is the value that we want to test
represent the significance level
Confidence=92% or 0.92
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion of defective is different from 0.05.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
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.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
If we compare the p value and the significance level given we have
so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 8% of significance the true proportion of defectives is different from 0.05.
