Chapter 10.2, Problem 57E

(a)

To determine

To explain: the reason for the random assignment of subjects by researchers to the two treatment classes.

Explanation of Solution

Subjects are assigned arbitrary to the two treatments in order to ensure that the two treatment groups are as identical as possible and to minimise the influence of any unmeasured variables.

(b)

To determine

To explain: the inference with suitable evidence will draw and justify the answer.

Answer to Problem 57E

The average is greater for students with internal reasons than for students with external reasons.

Explanation of Solution

Given:

  

It is noticed on the dot plot that almost no dots lay above 4.15 and to the right of it. This suggests that the sample mean difference of 4.15 is unusual and therefore we infer that, and those with internal reasons, the mean tends to be significantly greater than and those with external reasons.

(c)

To determine

To Explain: the error that make type I error or type II error on the basis of given information.

Answer to Problem 57E

Type I error

Explanation of Solution

The hypothesis testing

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_1:{\mu }_1>{\mu }_2\end{array}$

It is concluded in part (b) that the means were significantly different and therefore dismissed the null hypothesis.

Type I error: Reject $H_0$ , if $H_0$ is true.

Type II error: Fail to reject $H_0$ , if $H_0$ is false.

Although, it is rejected null hypothesis $H_0$ , it may have made a type I error.