Mathematics, 14.02.2020 19:57 acoverupoze5th

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.

Answers: 2

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Answers

Answer from: MJyoungboy

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

$\hat p$ 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:

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

Answer from: Quest

Hello!

the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

$\frac{a^{m} }{a^{n} }=a^{m-n}$

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

$\frac{3^{4} }{3^{1}}$