Suppose that you have bivariate data for an entire population.

a. How would you decide whether an association exists between the two variables under consideration?

b. Assuming that you make no calculation mistakes, could your conclusion be in error? Explain your answer.

Short Answer

Expert verified

Part a. If all the conditional distributions are identical then no association exists between the two variables, otherwise, there is an association between the two variables.

Part b. No, because the data are for an entire population, no inference is being made from a sample to the population, the conclusion is a fact.

Step by step solution

01

Part (a) Step 1. Given Information

We are given a bivariate data for an entire population.

02

Part (a) Step 2. Explanation

To decide whether an association exists between the two variables under consideration first we obtain the conditional distribution of one of the variables for each possible value of the other variable.

If all the conditional distributions are identical then no association exists between the two variables, otherwise, there is an association between the two variables.

03

Part (b) Step 1. Explanation

If a calculation mistake is done then your conclusion could not be in error.

This is because the data are for an entire population, no inference is being made from a sample to the population, the conclusion is a fact.

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 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

In each of the given Exercises, we have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 to be satisfied. Note: The number of cells for a contingency table with m rows and n columns is m⋅n.

12.71 two and three

In Exercises 12.101-12.106, tase either the critical-value approach or the P-value approach to perform a chi-square homogeneity test, provided the conditions for using the test are met.
12.101 Self-Concept and Sightedness. Self-concept can be defined as the general view of oneself in terms of personal value and capabilities. A study of whether visual impairment affects self-concept was reported in the article "An Exploration into Self Concept: A Comrarative Analysis between the Adolescents Who Are Sighted and
Elind in India" (British Journal of Visual Impairment, Vol. 30, No. 1, of sighted and blind Indian adolescents gave the following data on self-concept.

a. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in self-concept distributions between sighted and blind Indian adolescents?
b. Repeat part (a) at the1%significance level.

Fill in the blank: If a variable has only two possible values, the chi-square homogeneity test provides a procedure for comparing several population......................................

Variegated Plants. Arabidopsis is a genus of flowering plants related to cabbage. A variegated mutant of the Arabidopsis has yellow streaks or marks. E. Miura et al. studied the origin of this variegated mutant in the article "The Balance between Protein Synthesis and Degradation in Chloroplasts Determines Leaf Variegation in Arabidopsis yellow variegated Mutants" (The Plant Cell, Vol. 19, No. 4, pp. 1313-1328). In a second-generation cross of variegated plants, 216 were variegated and 84 were normal. Genetics predicts that 75% of crossed variegated plants would be variegated and 25% would be normal. At the 10% significance level, do the data provide sufficient evidence to conclude that the second generation of crossed variegated plants does not follow the genetic predictions?

In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.

Distribution: 0.2,0.1,0.1,0.3,0.3

Observed frequencies: 29,13,5,25,28

Significance level =0.10

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.

Sign-up for free