Answer:
a) Two tailed test
Null hypothesis:
Alternative hypothesis:
b)
c) If we compare the p value obtained and the significance level given
we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
We Fail to reject the null hypothesis H0
Explanation:
Data given and notation
n represent the random sample taken
X represent the outcomes desired in the sample
estimated proportion of interest
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
z would represent the statistic (variable of interest)
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 proportion is 0.217 or no:
a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.
Two tailed test
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, 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
.
Calculate the statistic
For this case the calculated value is given z =2.17
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.
b. Find the P-value
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:
c. Using a significance level of alphaαequals=0.01, should we reject Upper H 0 or should we fail to reject Upper H 0?
If we compare the p value obtained and the significance level given
we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
We Fail to reject the null hypothesis H0