Question

According to creditcard , the mean outstanding credit card debt of college undergraduate was $3173 in 2010. A researcher believes that this amount has decreased since then.
Required:
a. Determine the null and alternative hypotheses.
b. Explain what it would mean to make a Type I and Type Il error.

Answer 1

Answer:

a. The null and alternative hypothesis can be written as:

$H_0: \mu=3173\\\\H_a:\mu< 3173$

b. A Type I error is made when a true null hypothesis is rejected. In this case, it would happen if it is concluded that the actual mean outstanding credit card debt of college undergraduate is significantly less than $3173, when in fact it does not.

A Type II error is made when a false null hypothesis is failed to be rejected. In this case, the actual mean outstanding credit card debt of college undergraduate is in fact less than $3173, but the test concludes there is no enough evidence to claim that.

Step-by-step explanation:

We have a prior study of the mean outstanding credit card debt of college undergraduate that states that it was $3173 in 2010.

A researcher believes that this amount has decreased since then.

Then, he has to perform a hypothesis test where the null hypothesis states that the mean is still $3173 and an alternative hypothesis that states that the actual credit card debt is significantly smaller than $3173.

The null and alternative hypothesis can be written as:

$H_0: \mu=3173\\\\H_a:\mu< 3173$