Question

Teacher Salaries. Refer to Exercise 9.22. Explain what each of the following would mean.

a. Type I error

b. Type II error

c. Correct decision

Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fast the mean salary of classroom teachers in Ohio

d. equals the national mean of \(55.4 thousand.

e. exceeds the national mean of \)55.4 thousand.

Short answer

(a) Rejecting a Null Hypothesis, when it is true.

(b) Rejecting a Null Hypothesis, when $\left(H\right)$is false.

(c) If the true null hypothesis is not rejected or a false null hypothesis is rejected.

(d) Type II error.

(e) Correct Decision.

Step-by-step solution

Step 1. Given

Here the null and alternative hypotheses are defined as follows:

H.: The mean annual salary of public in class room teachers is equal to the national salary of teachers $49.0.

$H_0:\mu =\$49$

H.: The mean annual salary of public class room teachers in is greater than the national salary of $49.0.

Versus,

$H_a:\mu =\$49$

Part (a) Type i error

According to the definition of the type I error; rejecting a null hypothesis, when it is true. A type one error would occur in fact $\mu =\$49.0$is true, that is the mean annual salary of public class room teachers in National survey of teachers in public schools is $49.0, but the results of the sampling lead to conclude that mean salary of school teachers is equal to $49.0, hence the rejection of true null hypothesis.

Part (b) Type II error

According to the definition of the type II error; not rejecting a null hypothesis, when it (H₁) is false. Here, a type II error would occur if in fact$\mu =\$49.0$ is not to be rejected, but the results of ။ the sampling fail to conclude that mean annual salary of public class room teachers in National

survey of teachers in public schools is $49.0.

Part (c) Correct decision

A correct decision would occur if true null hypothesis is not rejected or a false null hypothesis is rejected. Here, in fact the mean annual salary of public class room teachers in National survey of teachers in public schools is $49.0, and the results of the sampling do not lead to the rejection, so which is a correct decision; or mean annual salary of public class room teachers in National survey of teachers in public schools differs from $49.0, and the results of the sampling lead to the rejection of the null hypothesis of $49.0.

Part (d) Classifying the error

Here the mean annual salary of public class room teachers in is $49.0, and the results of a hypothesis test lead to non rejection of the null hypothesis. We need to classify the decision as an error type or a correct decision.

As a sampling result we obtain the mean annual salary of public class room teachers in Hawaii in public schools is $49.0, and we are not rejecting the null hypothesis that the mean annual salary of public class room teachers in National survey of teachers in public schools is $49.0, that is the true null hypothesis is not rejected, So we are taking correct decision.

Part (e) Classifying the error

Here the mean annual salary of public class room teachers in exceeds $49.0, and the results of a hypothesis test lead to non rejection of the null hypothesis. We need to classify the decision as an error type or a correct decision.

We are not rejecting the null hypothesis of $\mu =\$49.0,$where we obtain as a sampling result that mean annual salary of public class room teachers in exceeds from $49.0. Therefore, we are committing type II error.