Chi-Square Test Questions: Expert Solutions

Table 1 gives the distribution of the number of acceptances of 100 students into 3 departments in College of Commerce and Business Administration. Test at the 5% level of significance that the distribution of acceptances is approximately binomial if the probability of a student's being accepted into college is 0.40.
What is the computed value of chi-square? Blank 1
What is the tabular value of chi-square? Blank 2
Choose a or b Blank 3
a. Accept the null hypothesis because the tabular value of chi-square is larger than the computed value of chi-square.
b. Accept the alternative hypothesis because the tabular value of chi-square is smaller than the computed value of chi-square.
$\begin{array}{|cc|}\hline \text{ Number of Acceptances }& \text{ Number of Students }\\ 0& 25\\ 1& 34\\ 2& 31\\ 3& 10\\ \hline\end{array}$

Suppose a researcher used a sample of 400 students to determine if there is a significant preference between 3 designs for a phone. If a calculated value of Chisquare of 9.07 is found, what decision should the researcher make?
A. There is a significant preference at both the .05 level of significance and the .01 level of significance
B. There is no significant preference at any level of significance
C. There is a significant preference at the .05 level of significance but not at the .01 level of significance
D. There is a significant preference at the .01 level of significance but not
at the .05 level of significance
11. What is indicated by an extremely large calculated value of Chi-square in a one-way Chi-square test?
A. There is a perfect match between the observed frequencies in the sample and the null hypothesis
B. The observed frequencies in the sample are very different from the expected frequency
C. The observed frequencies in the sample are very similar to the expected frequency
D. None of the above
12. Suppose a researcher is using a two-way Chi-square test to evaluate the relationship between birth-order position and self-esteem. Each participant is classified as being 1st born, 2nd born, or 3rd born, and self-esteem is categorized as being low, medium, or high. In this study, the number of degree(s) of freedom (df) would be:
A. 1
B. 4
C. 3
D. 2

Explain why a chi-square goodness-of-fit test, a chi-square independence test, or a chi-square homogeneity test is always right tailed.

Explain what chi squared goodness of fit 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 goodness of fit test.

The chi-square test is appropriate for use when:
you have one categorical independent variable and one numerical scaled dependent variable.
you have the dependent and independent variables need to be measured on an interval or ratio scale.
you have data from two numerical variables.
you have data from two categorial variables.

Suppose a two-way Chi-square test is used to evaluate the relationship between two variables. If both variables have 4 categories or 'items', the number of degrees of freedom (df) for the Chi-square test would be:
A. 8
B. 7
C. 4
D. 9
In a two-way Chi-square situation, you are trying to determine if there is a significant relationship between two variables that represent the nominal and/or ordinal scale of measurement.
A. True
B. False
What is stated by the null hypothesis in a two-way Chi-square test?
A. The two variables have a curvilinear relationship
B. The two variables have very different frequency distributions
C. There is a significant relationship between the two variables
D. There is no significant relationship between the two variables

Suppose that you are interested in examining the relationship between executive compensation and three independent variables that you believe have an effect: Proficiency in a second language, education level, and work experience abroad. You want to be sure, however, that conditional heteroscedasticity is not present in your data. Therefore, you regress the squared residuals of the regression model onto the three independent variables, and you find that the ${\displaystyle R^2}$ for the regression 0.181. Your sample size of executives is 36.
a. What is the name of the test that is used to determine if conditional heteroscedasticity is present?
b. Using the information provided, calculate the F-statistic that you would use to determine if there is conditional heteroskedasticity present.
c. Using the information provided, calculate the ${\displaystyle {\chi }^2}$ test statistic (LM method) that you would use to determine if there is conditional heteroskedasticity present.
d. What critical value would you use if you are testing at a 5% significance level using the F-test approach?
e. What critical value would you use if you are testing at a 5% significance level using the ${\displaystyle {\chi }^2}$ test approach?

The degrees of freedom in a chi-squared test equal to the number of participants in the test minus 1.

The _(1)_ are the data for a Chi-Square test, and you get them by simply counting. The _(2)_ are something you get from either past research, or an assumption that all categories are equal, and they go in the null hypothesis. The _(3)_ are something you get by multiplying sample size, n, by expected proportions.
Group of answer choices:
(1) observed frequencies, ${\displaystyle f_o}$ (2) expected proportions (3) expected frequencies, ${\displaystyle f_e}$
(1) expected frequencies, ${\displaystyle f_e}$ (2) expected proportions (3) observed frequencies, ${\displaystyle f_o}$
(1) expected proportions (2) observed frequencies, ${\displaystyle f_o}$ (3) expected frequencies, ${\displaystyle f_e}$
(1) expected frequencies, ${\displaystyle f_e}$ (2) observed frequencies, ${\displaystyle f_o}$ (3) expected proportions

The Bitter Bottling Company has developed "Featherweight," the cola with fewer calories and less taste. To evaluate this new product, the marketing manager gives a taste test to a random sample of 300 people. Each person in the sample tastes Featherweight and 4 other diet cola brands. To avoid bias, the actual brand labels are replaced by the letters A, B, C, D, and E. The results of the sample are shown in the following table:
$\begin{array}{|cc|}\hline \text{ Brand }& \text{ Number of Preferring Brand }\\ \text{ A }& 50\\ \text{ B }& 65\\ \text{ C }& 45\\ \text{ D }& 70\\ \text{ E }& 70\\ \hline\end{array}$
Do the customers prefer a particular brand more than the others?
Use an alpha of 0.05.
1.What type of hypothesis testing should be used?
a. Chi-square Goodness of Fit Test
b. Chi-square Test on Independence
2. What are the null and alternative hypothesis?
a. ${\displaystyle H_0}$: The market does not have preferences; ${\displaystyle H_1}$: The market does have preference
b. ${\displaystyle H_0}$: The market does have preferences; ${\displaystyle H_1}$: The market does not have preference
3. What are the significance level and the type of test?
a. ${\displaystyle \alpha =0.05}$, Right-tailed
b. ${\displaystyle \alpha =0.05}$, left-tailed
c. ${\displaystyle \alpha =0.05}$, two-tailed

Suppose we wanted to see if there was a correlation between suspension and ethnicity. We have the following summary of data below. What statistical test would we use?
$\begin{array}{|ccc|}\hline & \text{ Suspended }& \text{ Note Suspended }\\ \text{ Black }& 17& 17\\ \text{ White }& 65& 878\\ \hline\end{array}$
Group of answer choices
No answer text provided.
Chi-squared
Z-test
T-test

The chi-square test can only be used when we have:
a. Actual frequencies (integer numbers)
b. Percentages
c. Proportions
d. Means
e. All of the above
4. The chi-square test is used to determine relationships between two or more:
a. Nominal variables
b. Numerical variables
c. Both nominal and numerical variables
d. None of the above

I need answer full parts to the question. Show all work and be neat. Show all conditions, and p-value, conclusion, anything under the 4 step statistical process. Thanks!
It can be difficult to motivate preschoolers to practice writing letters. Perhaps a reward system will do the trick, but what type of rewards work? Here are the data from a randomized experiment that compared three treatments among children in preschool. A “success" means that the child completed a worksheet in which they traced the entire alphabet in one sitting.
$\begin{array}{|cccc|}\hline \text{Group}& \text{Reward}& \text{Subjects}& \text{Successes}\\ 1& \text{Choice of a small toy}& 20& 13\\ 2& \text{Choice of candy}& 24& 18\\ 3& \text{Promise of immediate recess}& 16& 10\\ \hline\end{array}$
(a) Which chi-square test is appropriate in this setting? Explain your reasoning
(b) State the appropriate hypotheses for performing a chi-square test in this setting.
(c) The chi-square test statistic is ${\displaystyle {\chi }^2=0.847}$. Calculate the P-value.
(d) Interpret the P-value
(e) What conclusion would you draw?

Suppose we observe the following random sample of size n = 117, sampled from a discrete distribution.
$\begin{array}{|cccccccc|}\hline \text{ Value }& 0& 1& 2& 3& 4& 5& 6\\ \text{ Count }& 32& 36& 21& 18& 6& 2& 2\\ \hline\end{array}$
We would like to test whether this data comes from a Poisson(${\displaystyle \lambda }$) distribution.
calculate the observed value of the appropriate Goodness of Fit test statistic, used to test the null hypothesis that the observed data is Poisson distributed.
Give answer to three decimal places. Compute the p-value of the observed test statistic you just computed. Give answer to three decimal places.

Suppose an investigator has studied the possible association between the use of a weight-loss drug and a rare central nervous system (CNS) disorder. He samples from a group of volunteers with and without the disorder, and records whether they have used the weight-loss drug.
The data are summarized in the attached table:
What is the estimated the odds ratio for the presence of a CNS disorder, comparing people who have used the weight-loss drug to those who have not? What test would you use to evaluate the null hypothesis of no association between weight-loss drug use and presence of a CNS disorder?
$\begin{array}{cc}& \text{Weight-Loss Drug Use}\\ & \begin{array}{|ccc|}\hline \text{ CNS disorder }& \text{ Yes }& \text{ No }\\ \text{ Yes }& 10& 2000\\ \text{ No }& 7& 4000\\ \hline\end{array}\end{array}$

I have some problems, help
In chi-square tests, the conventional and conservative rule is to require that the difference between the observed and expected frequency for each cell be at least 5.
1. True
2. False

Resources O Hint Press Esc to exit full screen Are younger people more likely to be vegan/vegetarian? To investigate, the Pew Research Center classified a random sample of 1480 U.S. adults according to their age group and whether or not they are vegan/vegetarian.
Determine which chi-square test is appropriate for the given setting. Which response below gives the correct test with appropriate reasoning?
a. Chi-square goodness of fit test because the data came from a single random sample with the individuals classified by their chocolate consumption.
b. Chi-square test for homogeneity because the data come from two independent random samples – those who are vegan/vegetarian and those who are not.
c. Chi-square test for homogeneity because the data came from a single random sample with the individuals classified according to two categorical variables.
d. Chi-square test for independence because the data came from a single random sample with the individuals classified according to two categorical variables.
e. Chi-square test for independence because the data come from two independent random samples – those who are vegan/vegetarian and those who are not.

Data was collected from a simple random sample of 200 cell phone users age 18 or older in the United States. Each user was categorized by age-group and by whether he or she uses a certain cell phone app. The table shown summarizes the data, with expected cell counts in parentheses.
$\begin{array}{cc}& \text{Uses Cell Phone App}\\ \text{Age-Group}& \begin{array}{|cccc|}\hline & \text{ Yes }& \text{ No }& \text{ Total }\\ \text{ Young Adults }& 4(15.2)& 76(64.8)& 80\\ \text{ Older Adults }& 29(19.38)& 73(82.62)& 102\\ \text{ Elderly Adults }& 5(3.42)& 13(14.58)& 18\\ \text{ Total }& 38& 162& 200\\ \hline\end{array}\end{array}$
Which statement is true about whether the conditions for a chi-square test for independence have been met?
a. All necessary conditions are satisfied to apply a chi-square test for independence between age-group and texting use by cell phone users.
b. The data from the different age-groups are not the result of independent random samples; therefore, the conditions for the test are not met.
c. The total sample size in one or more of the age-groups is too small to meet the conditions of the chi-square test for independence.
d. Not all of the observed cell counts are large enough to satisfy the conditions for the chi-square test for independence.
e. Not all of the expected cell counts are large enough to satisfy the conditions for the chi-square test for independence.

Provide a thorough response to the two following questions.
1. What is hypothesis testing? Provide all basic components, including error types, with explanations.
2.What is the difference between chi-square goodness of fit and chi-square test of independence? What do they have in common?