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.

Wing Length. D. Cristol et al. published results of their studies of two subspecies of dark-eyed juncos in the paper "Migratory Dark-Eyed Juncos, Junco hyemalis, Have Better Spatial Memory and Denser Hippocampal Neurons Than Nonmigratory Conspecifics" (Animal Behaviour, Vol. 66, Issue 2, pp. 317-328). One of the subspecies migrates each year, and the other does not migrate. A hypothesis test is to be performed to decide whether the mean wing lengths for the two subspecies (migratory and nonmigratory) are different.

Short answer

Part a. The variable is wing length.

Part b. The two populations are migratory subspecies and nonmigratory subspecies.

Part c. Null hypothesis $H_0:{\mu }_1={\mu }_2$and alternative hypothesis $H_a:{\mu }_1\ne {\mu }_2$

Part d. The hypothesis is classified as two-tailed.

Step-by-step solution

Part (a) Step 1. Given Information 

We are given a hypothesis.

A hypothesis test is to be performed to decide whether the mean wing lengths for the two subspecies (migratory and nonmigratory) are different.

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.

The wing lengths of two subspecies are recorded in the article.

So the variable in this study is wing lengths

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.

Wing lengths of two subspecies are recorded. They are migratory subspecies and nonmigratory subspecies.

So the two populations are migratory subspecies and nonmigratory subspecies.

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

Let us assume that ${\mu }_1$denotes the mean wing length of migratory subspecies and ${\mu }_2$denotes the mean wing length of nonmigratory subspecies.

The null hypothesis is defined as

$H_0:$There is no significant difference between the mean wing length of migratory subspecies and nonmigratory subspecies.

$H_0:{\mu }_1={\mu }_2$

The alternative hypothesis is defined as

role="math" localid="1652781176688" $H_a:$There is a significant difference between the mean wing length of migratory subspecies and nonmigratory subspecies.

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

Part (d) Step 1. Classification   

As our alternative hypothesis suggest that the mean of the first population is not equal to the mean of the second population.

So the hypothesis can be classified as a two-tailed test.