Answer:
D. We cannot conclude that more than 15% of the population has at least one sibling.
Step-by-step explanation:
Data given and notation
n represent the random sample taken
X represent the number of people who has at least one sibling
estimated proportion of people who has at least one sibling
is the value that we want to test
represent the significance level
Confidence=90% or 0.90
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 true proportion of people who has at least one sibling is more than 0.15:
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
.
Calculate the statistic
Let's assume that the calculated value for this case is
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 right tailed test the p value would be:
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the proportion of people who has at least one sibling is not significanlty higher than 0.15.
So then the best answer for this case would be:
D. We cannot conclude that more than 15% of the population has at least one sibling.