Chapter 10, Problem 1RE

(a)

To determine

The null hypothesis H₀ and the alternative hypothesis H₁.

Answer to Problem 1RE

Solution: The null and alternative hypothesis are

$H_0:\mu =\$3173$

and

$H_1:\mu <\$3173$

Explanation of Solution

Given: The mean of credit card debt of UG was $3173.

Explanation: In the study, $\mu$ is the mean of credit card debt of college students, $\overline{x}$ is the sample mean in the study and n is the sample size. The researcher believes that the amount was $3,173 in 2010, that is $\left(H_0:\mu =\$3173\right)$, and this amount has decreased by $3173, that is, $\left(H_1:\mu <\$3173\right)$.

(b)

To determine

To explain: The type I error in this study.

Answer to Problem 1RE

Solution: The null hypothesis H₀ is rejected when the mean credit card of college UG students has not reduced. Thus, it can be a type I error.

Explanation of Solution

The type I error is defined as

$\alpha =P\left(\text{Type I error}\right)$

(c)

To determine

To explain: The type II error in this study.

Answer to Problem 1RE

Solution: The null hypothesis H₀ is not rejected when the mean credit card of college UG students has reduced. Thus, it can be a type II error.

Explanation of Solution

The type II error is defined as

$\beta =P\left(\text{Type II error}\right)$

(d)

To determine

To state: The conclusion if H₀ is not rejected.

Answer to Problem 1RE

Solution: There is not enough evidence at the significance level to support the researcher’s opinion.

Explanation of Solution

In testing of a hypothesis, it is essential to remember that the null hypothesis cannot be accepted because without taking access to the whole population, the particular value of the parameter is not known.

(e)

To determine

To state: The conclusion if H₀ is rejected.

Answer to Problem 1RE

Solution: There is enough evidence at the significance level to support the researcher’s opinion.

Explanation of Solution

In testing of a hypothesis, it is essential to remember that the null hypothesis cannot be accepted because without taking access to the whole population, the particular value of the parameter is not known.