Question

Let Y be a random variable. Consider the following hypothesis​ test:

H0: E(Y)=μy,0H1: E(Y)≠μy,0

where H0 is the null hypothesis and H1 is the alternative hypothesis.

Which of the following statements are true about the null and alternative​hypothesis?​ (Check all that​ apply.)

a.The null hypothesis is that the population mean ​E(Y) takes on a specific value whereas the alternative hypothesis specifies what is true if the null hypothesis is not.



b.Hypothesis testing entails using data to provide sufficient evidence against both the null and alternative hypothesis.



c.Hypothesis testing entails using data to provide sufficient evidence against the null hypothesis and in favor of the alternative hypothesis.



d.Hypothesis testing entails using data to provide sufficient evidence in favor of both the null and alternative hypothesis.

Answer 1

a. The null hypothesis is that the population mean ​E(Y) takes on a specific value whereas the alternative hypothesis specifies what is true if the null hypothesis is not.

c. Hypothesis testing entails using data to provide sufficient evidence against the null hypothesis and in favor of the alternative hypothesis.

Explanation:

The null hypothesis shows that population mean is equal to specified value while alternative hypothesis shows that population mean is not equal to specified value . If the null hypothesis is rejected then the alternative hypothesis is considered true. So, the statement in option a is true about the null and alternative hypothesis.

Also, in hypothesis testing we use data to build sufficient evidence against the null hypothesis and if the sufficient evidence against null hypothesis is built then it means that evidence is in favor of alternative hypothesis. So, the statement in option c is also true.

So, the statements in option b and option c are true.