Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 7: Q110S (page 441)

Which of the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test

Short Answer

Expert verified

The elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test are null hypothesis, alternative hypothesis, test statistic, and rejection region.

Step by step solution

01

Given information

The information regarding the test hypothesis.

The test hypothesis can be used to conduct the test.

02

State the statistical hypothesis test

Hypothesis testing is a method in which statistical data from a group sample is drawn to reach a conclusion about population parameters. Generally, it is used when you want to compare two or more groups.

03

Explain the elements of a test hypothesis used to conduct the test prior to analyzing the data

Before performing any test of hypothesis, we must specify the null and alternative hypothesis as well as the desired level of significance α.

The given four elements are specified before the sampling experiment is performed.

Null Hypothesis (H0):

The null hypothesis is the theory about the specific values of one or more population parameters. The theory is always stated as H0: parameter=value.

Alternative Hypothesis (Ha):

The alternative hypothesis is a theory that contradicts the null hypothesis. The theory represents that which we will adopt only when sufficient evidence exists to establish its truth.

Test statistic:

A sample statistic is used to decide whether to reject the null hypothesis.

Rejection region:

The numerical values of the test statistic for which the null hypothesis will be rejected.

Hence, the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test are null hypothesis, alternative hypothesis, test statistic, and rejection region.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Hotels’ use of ecolabels. Refer to the Journal of Vacation Marketing (January 2016) study of travelers’ familiarity with ecolabels used by hotels, Exercise 2.64 (p. 104). Recall that adult travelers were shown a list of 6 different ecolabels, and asked, “Suppose the response is measured on a continuous scale from 10 (not familiar at all) to 50 (very familiar).” The mean and standard deviation for the Energy Star ecolabel are 44 and 1.5, respectively. Assume the distribution of the responses is approximately normally distributed.

a. Find the probability that a response to Energy Star exceeds 43.

b. Find the probability that a response to Energy Star falls between 42 and 45. c. If you observe a response of 35 to an ecolabel, do you think it is likely that the ecolabel was Energy Star? Explain.

Stability of compounds in new drugs. Refer to the ACS Medicinal Chemistry Letters (Vol. 1, 2010) study of the metabolic stability of drugs, Exercise 2.22 (p. 83). Recall that two important values computed from the testing phase are the fraction of compound unbound to plasma (fup) and the fraction of compound unbound to microsomes (fumic). A key formula for assessing stability assumes that the fup/fumic ratio is 1:1. Pharmacologists at Pfizer Global Research and Development tested 416 drugs and reported the fup/fumic ratio for each. These data are saved in the FUP file, and summary statistics are provided in the accompanying Minitab printout. Suppose the pharmacologists want to determine if the true mean ratio, μ, differs from 1.

a. Specify the null and alternative hypotheses for this test.

b. Descriptive statistics for the sample ratios are provided in the Minitab printout on page 410. Note that the sample mean,\(\overline x = .327\)is less than 1. Consequently, a pharmacologist wants to reject the null hypothesis. What are the problems with using such a decision rule?

c. Locate values of the test statistic and corresponding p-value on the printout.

d. Select a value of\(\alpha \)the probability of a Type I error. Interpret this value in the words of the problem.

e. Give the appropriate conclusion based on the results of parts c and d.

f. What conditions must be satisfied for the test results to be valid?

Latex allergy in health care workers. Refer to the Current Allergy & Clinical Immunology (March 2004) study of n = 46 hospital employees who were diagnosed with a latex allergy from exposure to the powder on latex gloves, Exercise 6.112 (p. 375). The number of latex gloves used per week by the sampled workers is summarized as follows: \(\bar x = 19.3\) and s = 11.9. Let \(\mu \) represent the mean number of latex gloves used per week by all hospital employees. Consider testing \({H_0}:\mu = 20\) against \({H_a}:\mu < 20.\)

a. Give the rejection region for the test at a significance level of \(\alpha = 0.01.\)

7.83 A random sample of n observations is selected from a normal population to test the null hypothesis that σ2=25 . Specify the rejection region for each of the following combinations of Ha,αand n.

a.Ha:σ2≠25;α=0.5;n=16

b. Ha:σ2>25;α=.01;n=23

c. Ha:σ2>25;α=.10;n=15

d. Ha:σ2<25;α=.01;n=13

e. Ha:σ2≠25;α=.10;n=7

f.Ha:σ2<25;α=.05;n=25

In a test of the hypothesis \({H_0}:\mu = 10\) versus \({H_a}:\mu \ne 10\), a sample of n = 50 observations possessed mean \(\bar x = 10.7\) and standard deviation s = 3.1. Find and interpret the p-value for this test.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation
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.

Sign-up for free