/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 10.30 In Exercises 10.25-10.30, hypoth... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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

Expert verified

Part a. The variable is wing length.

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

Part c. Null hypothesis H0:μ1=μ2and alternative hypothesis Ha:μ1≠μ2

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

Step by step solution

01

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.

02

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

03

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.

04

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

Let us assume that μ1denotes the mean wing length of migratory subspecies and μ2denotes the mean wing length of nonmigratory subspecies.

The null hypothesis is defined as

H0:There is no significant difference between the mean wing length of migratory subspecies and nonmigratory subspecies.

H0:μ1=μ2

The alternative hypothesis is defined as

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

Ha:μ1≠μ2

05

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In each of exercise 10.13-10.18, we have presented a confidence interval for the difference,μ1andμ2, between two population means. interpret each confidence interval.

95%CI is from-20to-15

The primary concern is deciding whether the mean of Population 1 differs from the mean of Population 2 .

A variable of two population has a mean of 7.9and standard deviation of 5.4for one of the population and a mean of 7.1and a standard deviation of 4.6 for the other population.

a. For independent samples of sizes 3and6respectively find the mean and standard deviation of x1-x2

b. Must the variable under consideration be normally distributed on each of the two population for you to answer part (a) ? Explain your answer.

b. Can you conclude that the variable x1-x2is normally distributed? Explain your answer.

Ha:μ1≠μ2

Right-Tailed Hypothesis Tests and CIs. If the assumptions for a pooled t-interval are satisfied, the formula for a (1-α)-level lower confidence bound for the difference, μ1-μ2, between two population means is

x¯1-x^2-ta·Sp1/n1+1/n2

For a right-tailed hypothesis test at the significance level α,

the null hypothesis H0:μ1=μ2will be rejected in favor of the alternative hypothesis Ha:μ1>μ2if and only if the (1-α)-level lower confidence bound for μ1-μ2is greater than or equal to 0. In each case, illustrate the preceding relationship by obtaining the appropriate lower confidence bound and comparing the result to the conclusion of the hypothesis test in the specified exercise.

a. Exercise 10.47

b. Exercise 10.50

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.