Chi-Square Test Questions: Expert Solutions

Use Table VII to find the required ${\displaystyle {\chi }^2}$-values. Illustrate your work graphically.
When you use chi-square procedures to make inferences about a population standard deviation, why should the variable under consideration be normally distributed or nearly so?

The table below shows the number of students absent from a college on particular days in a semester.
$\begin{array}{|ccccccc|}\hline \text{ Day }& \text{ Sun }& \text{ Mon }& \text{ Tue }& \text{ Wed }& \text{ Thu }& \text{ Total }\\ \text{ Frequency }& 100& 80& 87& 103& 110& 480\\ \hline\end{array}$
Use chi-square goodness of fit test to test the claim that the absence is distributed equally among the days at 0.05 level of significance.

To test if TV preference and gender are independent, which hypothesis test would be used?
a. 2 Prop Z Test
b. Chi-square test
c. ! Sample T test
d. Linear Regression Test

The Pour It On marketing company is investigating whether the type of house and the color of a house in a certain town are related. Assume the conditions for inference are met.
Which of the following significance tests would be the most appropriate to use to determine whether there is an association between type of house and color of a house?
a. A two-sample t-test for mean.
b. A two sample z-test for mean.
c. Aregression t-test.
d. A chi-square goodness-of-fit test.
e. A chi-square test of independence.

The number of degrees of freedom associated with the chi-square distribution in a test of independence is
a. number of sample items minus 1.
b. number of populations minus number of estimated parameters minus 1.
c. number of populations minus 1.
d. number of rows minus 1 times number of columns minus 1.

Identify an appropriate statistical test and the tail of the test for the following problems. Assume all samples used for the study come from a normal population.
A. Determine if the performance of ABCS 206 students in an interim assessment(IA) is a good predictor of their performance at the end of semester examination.
B. A hair cream manufacturer wants to know if there is a relationship between the quantity of hair cream applied to the hair and the growth of hair.
C. A district health officer wishes to determine if the six villages in his district are independent of residents contracting malaria, schistosomiasis, cholera or tuberculosis.
D. A biologist is studying three different varieties of tomato to determine whether there is a difference in the proportion of seeds that germinate. Random samples of 200 seeds of each of three varieties are subjected to the same starting conditions.

There are 209 dogs who participate in a training to become service dogs.
There are four breeds of dogs.
Some dogs pass the certification test and some do not?
Chi square question:
Is there an association between breed of dog and passing the test? Or, are breed and passing the test independent of each other?
Blank tables are provided for your calculations.
1. What are the null and alternative hypotheses for the chi square test of independence?
2. Calculate the expected frequencies for each “cell”
3. Using the steps shown in the lecture and in the text, calculate the chi square to investigate whether “passed certification” and “breed of dog” are independent of each other or not.
4. Compare your calculated chi square to the critical value of chi square per the table, using the correct degrees of freedom.
$\begin{array}{|cccccc|}\hline & \text{ Chihuahua }& \text{ French Bulldog }& \text{ Golden Retriever }& \text{ Terriers }& \text{ Total }\\ \text{ Trained and certified as therapy dog }& 20& 12& 50& 37& 119\\ \text{ Trained but not certified as therapy dog }& 15& 15& 37& 23& 90\\ \text{ Total who took the training }& 35& 27& 87& 60& 209\\ \hline\end{array}$

The results of a significance test for the difference of two proportions would be the same as a chi-squared test for independence for two variables with two levels.
Group of answer choices:
-True
-False
If one of the categorical variables has 3 or more levels then we can consider the difference of proportions and use the normal distribution to determine the p-value.
Group of answer choices:
-True
-False
If the results of the chi-squared test for independence turn out to be significant then we can guarantee the variables are dependent.
Group of answer choices:
-True
-False

For a goodness-of-fit test with ${\displaystyle \alpha =0.10}$ and 5 categories, what is the critical χ2 value?

Identify a correct test to use to test the claim (some claims may be tested using more than one test). Assume al assumptions for the tests are met. Tests may be used more than once or not at all.
a. One sample t-test
b. Two sample t-test
c. Matched pairs test
d. One sample proportion z-test
e. Two sample proportion z-test
f. Slope t-test for linear regression
g. ANOVA test for linear regression
h. One-way ANOVA
i. Chi-square test for independence
j. Chi-square test for goodness of fit
A. The distribution of Starburst colors is 25% red, 25% orange, 25% pink, and 25% yellow.
B. Gas costs more, per gallon, at Shell stations than at Mobil stations across the street from them
C. There is no relationship between how much you eat (in calories) and your weight.
D. When people experience pain, they report less pain when they swear than when they don't swear.
E. One-third of American adults can't identify the United States on a world map.
F. Men are more likely to drive and text than women are.
G. Undergraduates in every CSUF College, on average, have the same GPA
H. On average, a "gallon of milk" contains less than 1 gallon.
I. Knowing your favorite burger chain tells me nothing about whether you prefer pancakes or waffles.
J. The more money you have, on average, the more problems you have.

For each of the following examples, state whether the chi-square goodness-of-fit or the chi-square test for independence is appropriate.
15a. An instructor tests whether class attendance (low, high) and grade point average (low, average, high) are independent.
A. goodness of fit test
B. test for independence
15b. An educator tests whether the teacher's speaking style (monotone, dynamic) and student interest (low, high) are independent.
A. goodness of fit test
B. test for independence
15c. A sports psychologist compares the number of athletes with Type A or Type B personality traits.
A. goodness of fit test
B. test for independence
Any help

Fingerprint analysis and blood grouping are features that do not change through the lifetime of an individual. Fingerprint features appear early in the development of a fetus, and blood types are determined by genetics. Therefore, each is considered an effective tool for identification of individuals. These characteristics are also of interest in the discipline of biological anthropology—a scientific discipline concerned with the biological and behavioral aspects of human beings.
(a) Is the test for an association in this case a chi-square test of independence, or a chi-square test of homogeneity? Justify your choice.
(b) Identify the conditions for the chi-square inference procedure selected in part (a), and indicate whether the conditions are met.
(c) The resulting chi-square test statistic from the appropriate test is approximately 18.930. What are the degrees of freedom and p-value of the test?
(d) Biological anthropology is concerned with the comparative study of human origin, evolution and diversity. Considering the sampling design in this study, to what population is it reasonable for the researchers to generalize their results?
$\begin{array}{|cccccc|}\hline & & \text{Blood Type}& & & \\ & A& B& AB& O& \text{Total}\\ \text{Loops}& 66(71.69)& 99(112.19)& 35(32.29)& 101(84.83)& 301\\ \text{Whorls}& 51(47.16)& 91(73.80)& 15(21.24)& 41(55.80)& 198\\ \text{Arches}& 14(12.15)& 15(19.01)& 9(5.47)& 13(14.37)& 51\\ \text{Total}& 131& 205& 59& 155& 550\\ \hline\end{array}$

If a chi-square test of Independence ends in a non-significant result it means that the variables depend on each other.
True or False

How to interpret the result according to the table below?
$\begin{array}{cc}& \text{Chi-square Tests}\\ & \begin{array}{|cccc|}\hline & \text{ Value }& \text{ df }& \text{ Asymptotic Significance (2-sided) }\\ \text{ Pearson Chi-Square }& & 2& .034\\ \text{ Likelihood Ratio }& & 2& .033\\ \text{ Linear-by-Linear Association }& & 1& .380\\ \text{ N of Valid Cases }& & & \\ \hline\end{array}\end{array}$
a) Since 0.034<0.05, the Ho hypothesis is rejected
b) Since 0.033<0.05, the Ho hypothesis is rejected
c) Since 0.034<0.5, the Ho hypothesis is rejected
d) Since 0.380>0.05, the Ho hypothesis is accepted
e) Since 0.033<0.5, the Ho hypothesis is rejected

Explain what chi-squared test of independence is. What is the underlying assumption? What is the test statistic and what is its asymptotic distribution? How the hypothesis is formulated and what are the expected outcomes? What is the criterion for rejecting the null hypothesis? How is the p value evaluated? Provide a hypothetical formulation of test of independence.

Explain the Chi – Square test and when it is appropriate.

Explain how the chi-square tests differ from parametric tests (such as t tests or ANOVA) with respect to the hypotheses, the data, and the assumptions underlying the test.

Employers want to know which days of the week employees are absent in a five-day work week. Most employers would like to believe that employees are absent equally during the week. Suppose a random sample of 61 managers were asked on which day of the week they had the highest number of employee absences. The results were distributed as in Table. For the population of employees, do the days for the highest number of absences occur with equal frequencies during a five-day work week? Test at a 0.05% significance level.
$\begin{array}{|cc|}\hline \text{ Day }& \text{ Observed Frequency }\\ \text{ Monday }& 6\\ \text{ Tuesday }& 14\\ \text{ Wednesday }& 15\\ \text{ Thursday }& 10\\ \text{ Friday }& 16\\ \hline\end{array}$
What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.)
${\displaystyle {\chi }^2=}$
What are the degrees of freedom for this test?
d.f.=
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value=

Egyptian fruit bats in the wild commonly eat loquats, figs and wild dates. Aresearcher wanted to see whether Egyptian fruit bats showed any preference amongthese three types of fruit. To test that, the researcher collected a sample of 60 fruit bats.Each bat was given an opportunity to select one of the three types of fruit, and its choicewas recorded. The following frequencies were observed:
$\begin{array}{|ccc|}\hline \text{ Loquats }& \text{ Figs }& \text{ Wild dates }\\ 12& 25& 23\\ \hline\end{array}$
a. What type of test should be used to analyze these data?
b. conduct the appropriate test

Explain what the purpose of chi-square is.
For a chi-square test, the observed frequencies are always whole numbers.TRUE or FALSE
For a chi-squares test, the expected frequencies are always whole numbers.TRUE or FALSE