Marvin Mccormick
2021-03-01
Answered

Explain the Chi – Square test.

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au4gsf

Answered 2021-03-02
Author has **95** answers

Step 1

Introduction:

The chi-square test can be used to test the in the following scenarios:

To test the Goodness of fit of the variables when their expected and observed frequencies are given.

To test the independence of the categorical variables by making it into a contingency table.

To test the significance of the single variance with the given variance.

1). Goodness of fit:

Goodness of fit test is applied to check how well the sample data obtained fits the distribution of the selected population. It can also be viewed as whether the frequency distribution fits the given pattern. Most commonly used test to check the goodness of fit is the chi-square test.

There are two values involved are observed and the expected values. The observed value represents the frequency of particular category in the sample and the expected value is obtained from the given distribution. Moreover, it summarizes the difference between the expected and observed values of the given data.

The hypotheses are stated as given below:

Null hypothesis: Data comes from the specified distribution.

Alternative hypothesis: Data does not come from the specified distribution.

The chi-square test statistic is calculated using the formula given below:

where,

Step 2

2). Test for independence:

In test for independence, we test whether there is an association between the categorical variables.

Null hypothesis: There is no association between the two categorical variables.

Alternative hypothesis: There is no association between the two categorical variables.

The chi-square test statistic is calculated using the formula given below:

where,

in

in

Step 3

3). Test for single variance:

Here, the chi-square test is used to compare the single sample variance with the population variance.

Null hypothesis: The given sample variance is equal to the population variance.

Alternative hypothesis: The given sample variance is not equal (less or greater) to the population variance.

The chi-square test statistic is calculated using the formula given below:

where,

n-Sample size

Step 4

Examples for some research questions based on chi square tests:

1.Is there significant association between blood pressure and exercise level?

2.Whether the class has less variation in statistics marks than the other past statistics classes marks?

3.To check whether health insurance benefits vary by the size of the company.

4.To test the claim that the subject distribution of books in the library fits the distribution of books checked out by students.

5.The level of education and the amount of proceeded foods in an individual’s diet are independent or not.

asked 2022-04-18

What happens to the critical value for a chi-square test if the number of categories is increased?

a. The critical value increases.

b. The critical value decreases.

c. The critical value depends on the sample size, not the number of categories.

d. The critical value is determined entirely by the alpha level

a. The critical value increases.

b. The critical value decreases.

c. The critical value depends on the sample size, not the number of categories.

d. The critical value is determined entirely by the alpha level

asked 2022-04-30

Let $p}_{1$ = population proportion for population 1, $p}_{2$ = population proportion for population 2, ... and $p}_{k$ = population proportion for population k. Consider the following null hypothesis: $H}_{0$ : $p}_{1$ =$p}_{2$ =...=$p}_{k$ . Which of the following statements is correct?

a. The alternative hypothesis to the null hypothesis stated above must be:$H}_{\alpha$ : Not all population proportions are equal.

b. If the sample data and the chi-square test computations indicate$H}_{0$ cannot be rejected, we cannot detect a difference among the k population proportions.

c. If the sample data and the chi-square test computations indicate$H}_{0$ can be rejected, we have the statistical evidence to conclude that one or more population proportions differ from the other population proportions.

d. All of the above.

a. The alternative hypothesis to the null hypothesis stated above must be:

b. If the sample data and the chi-square test computations indicate

c. If the sample data and the chi-square test computations indicate

d. All of the above.

asked 2022-03-19

Choose the appropriate test for the following situation: You wish to test whether an association exists between the type of vehicle purchased and how many children the buyer has.

a) Chi-square test

b) One-sample t-test

c) Two-sample t-test

d) ANOVA

a) Chi-square test

b) One-sample t-test

c) Two-sample t-test

d) ANOVA

asked 2022-03-08

Why would we want to use a Chi Squared Test for this study? What are the best ways to describe the data graphically and numerically?

An investigation of the association between drink preferences and the color of teeth is proposed. Subjects will be surveyed as to the type of drink most often consumed (coffee/tea. Juice, caramel-colored soda, water, or milk). A clinical exam will be performed after dental cleaning to determine the color of the teeth (reddish brown, reddish yellow, gray, reddish gray).

An investigation of the association between drink preferences and the color of teeth is proposed. Subjects will be surveyed as to the type of drink most often consumed (coffee/tea. Juice, caramel-colored soda, water, or milk). A clinical exam will be performed after dental cleaning to determine the color of the teeth (reddish brown, reddish yellow, gray, reddish gray).

asked 2022-03-18

A state is considering legislation to establisha law to help homeless individuals. A sample of 309 individuals regarding their opinions on the potential new law. Is there a relationship between sex and support for this law? Calculate the expected frequencies and compute a chi-square test for a statistically significant relationship between sex and support for the new law. Be sure to round to the second decimal.

$\begin{array}{cc}& \text{Sex}\\ \text{Support}& \begin{array}{|ccc|}\hline & \text{Male}& \text{Female}\\ \text{For}& 98& 101\\ \text{Against}& 29& 81\\ \hline\end{array}\text{}\end{array}$

asked 2022-03-26

David, a first year college student, is currently completing his statistics assignment but he is not understanding the notes about chi-square distribution.

c. Explain the following steps involved in a chi-square test of independence:

i) Identify the claim then state the null and alternative hypotheses (HoandHa) for this test.

ii) Select the level of significance.

iii) Calculate the test statistic.

iv) Formulate the Decision Rule and Make a Decision.

v) Interpret your decision in terms of the claim.

c. Explain the following steps involved in a chi-square test of independence:

i) Identify the claim then state the null and alternative hypotheses (HoandHa) for this test.

ii) Select the level of significance.

iii) Calculate the test statistic.

iv) Formulate the Decision Rule and Make a Decision.

v) Interpret your decision in terms of the claim.

asked 2022-03-15

What is the idea behind the chi–square test for independence?

a. To compare the cumulative distribution with what would be expected under independence

b. To compare the actual counts in a contingency table with what would be expected under independence

c. To compare the normal distribution with a chi-squared distribution

d. To compare the quantile-quantile (Q-Q) plot with what would be expected under independence

a. To compare the cumulative distribution with what would be expected under independence

b. To compare the actual counts in a contingency table with what would be expected under independence

c. To compare the normal distribution with a chi-squared distribution

d. To compare the quantile-quantile (Q-Q) plot with what would be expected under independence