Question

In Exercises 10.25-10.30, hypothesis tests are proposed. For each

hypothesis test,

a. identify the variable.

b. identify the two populations,

c. determine the null and alternative hypotheses.

d. classify the hypothesis test as two-tailed, left-tailed, or right-tailed.

Teaching Duties. Contingent faculty members in higher education are non-tenure track faculty, adjuncts, postdocs, lecturers, of instructors. R. Bowden and L. Gonzalez researched whether contingent faculty members are different from tenure-track faculty members with regards to teaching, research, and service in the article "The Rise of Contingent Faculty: Its Impact on the Professoriate and Higher Education" (Journal of Applied Research in Higher Education, Vol. 4, No. 1, pp. 5-22). A hypothesis test was conducted to decide whether the mean number of classes taught for credit per semester was less for contingent faculty than for tenure-track faculty.

Short answer

Part a. The variable in this study is the number of classes taught for credit per semester.

Part b. The two populations in this study are contingent faculty and tenure-track faculty.

Part c. Null Hypothesis$H_0:{\mu }_1={\mu }_2$

and alternative hypothesis $H_a:{\mu }_1<{\mu }_2$

Part d. The hypothesis test is left-tailed test.

Step-by-step solution

Part (a) Step 1. Given Information

We have been proposed a hypothesis test.

A hypothesis test was conducted to decide whether the mean number of classes taught for credit per semester was less for contingent faculty than for tenure-track faculty.

Part (a) Step 2. Identify the variable 

A variable is an attribute or a characteristic that can be measured. The value of the variable may differ for each and every unit. That is, a variable is defined as the characteristic which is recorded for each case.

In the given study, the number of classes taught for credit per semester was measured. It is clear that the number of classes taught for credit per semester varies from class to class. Hence, the variable is the number of classes taught for credit per semester.

Part (b) Step 1. Identify the two populations 

The population includes all the individuals of interest that are being examined. In other words, the collection of all people, items, or objects that are required for a specific study is defined as the population.

Here, the given study involves contingent faculty members and tenure-track faculty. Thus, the population is contingent faculty and tenure-track faculty.

Part (c) Step 1. Determine the null and alternative hypothesis 

Let us assume that ${\mu }_1$denotes the mean number of classes taught for credit per semester for contingent faculty and ${\mu }_2$denotes the mean number of classes taught for credit per semester for tenure-track faculty.

The null hypothesis is defined as

$H_0:$There is no significant difference between the mean mean number of classes taught for credit per semester for contingent faculty and tenure-track faculty.

role="math" localid="1652713151489" $H_0:{\mu }_1={\mu }_2$

The alternative hypothesis is defined as

$H_a:$The mean mean number of classes taught for credit per semester was less for contingent faculty than for tenure-track faculty.

$H_a:{\mu }_1<{\mu }_2$

Part (d) Step 1. Classification 

As our alternative hypothesis suggest that the mean of the first population is less than the mean of the second population.

So the hypothesis can be classified as left-tailed test.