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A hypothesis test is conducted with a significance level of 10%. The alternative hypothesis states that more than 15% of a population has at least one sibling. The p-value for the test is calculated to be 0.27. Which statement is correct?

A. We can conclude that more than 27% of the population has at least one sibling.

B. We can conclude that exactly 27% of the population has at least one sibling.

C. We can conclude that more than 15% of the population has at least one sibling.

D. We cannot conclude that more than 15% of the population has at least one sibling.

E. There is not enough information given to make a conclusion.

1 Answer

4 votes

Answer:

D. We cannot conclude that more than 15% of the population has at least one sibling.

Explanation:

Data given and notation

n represent the random sample taken

X represent the number of people who has at least one sibling


\hat p estimated proportion of people who has at least one sibling


p_o=0.15 is the value that we want to test


\alpha=0.1 represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)


p_v 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:
p\leq 0.15

Alternative hypothesis:
p > 0.15

When we conduct a proportion test we need to use the z statistic, and the is given by:


z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}} (1)

The One-Sample Proportion Test is used to assess whether a population proportion
\hat p is significantly different from a hypothesized value
p_o.

Calculate the statistic

Let's assume that the calculated value for this case is
z_(calc)

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
\alpha=0.1. The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:


p_v =P(z> z_(calc))=0.27

So the p value obtained was a very high value and using the significance level given
\alpha=0.1 we have
p_v>\alpha 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.

User Ricky Stewart
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