Answer:
Step-by-step explanation:
1) Data given and notation n
n represent the random sample taken
Xrepresent the people with a characterisitc in the sample
estimated proportion of people with the characteristic desired
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic
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 population proportionis higher than 0.554.:
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
The value of the statisitc is already calculate and given:
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 one right tailed test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we don't have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly higher than 0.554 .