Chi-Square Test Questions: Expert Solutions

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

What kinds of research questions are appropriate to use with a chi-square analysis?

when finding the p-value of a chi-square test, we always shade the tail areas in both tails.
Its true or false, help

When is it appropriate to use the chi-square test of Independence?

Which of the following test a chi-square distribution cannot be applied?
a. test of independence of two variables
b. test for the difference between two proportions
c. test for proportions of a multinomial population
d. test for the difference between two means

What statistic would you use if you had one independent variable ‘geographic location’ (North, South, East, West), and one dependent variable ‘satisfaction with living environment’ (Yes, No)? Explain why.

Which chi-square test should be used on the following study?
A psychotherapist wanted to see what percentages that patients sought after four different kinds of therapy consisting of play, dance, music and group therapy.
a.goodness of fit
b.test of independence

Which of the following statement is FALSE about the Chi-square test?
a. Chi-square test assumes one non-random sample is drawn from an independent population.
b. Chi-square test is used to compare observed frequencies in several categories corresponding with expected frequencies.
c. If more than 20% of the expected frequencies are less than 5, the Chi-square test is not recommended.
d. The data in a contingency table must be in the form of counts for the Chi-square to be valid.

Which would be the appropriate way to test differences in proportions for more than two samples?
a. t-test if variance is unknown
b. z-test
c. paired t-test
d. F-test for equality of variances
e. cross-tabulation procedure to conduct a chi-square test

Which of the statements are correct?
1 .A condition for using the chi-square goodness-of-fit test is that all expected counts must be at least five.
2. The chi-square goodness-of-fit test uses 1 - n degrees of freedom.
3. A condition for using the chi-square goodness-of-fit test is the observations are based on a random sample.
a. I only
b. II only
c. I and III only
d. II and III only
e. I, II, and III

When conducting a chi-square test of independence in a contingency table, as the difference between observed frequency and expected frequency ____, the probability of rejecting the null hypothesis increases.
a) stays the same
b) decreases
c) increases
d) goes to 0

When we carry out a chi-square goodness-of-fit test for a normal distribution, the null hypothesis states that the population?

When to use a chi- square test?

Which of the following is an assumption required by the chi-square test?
a. small samples
b. the frequencies in each cell are relatively similar
c. the sample was randomly selected
d. the variables are normally distributed

Which test? For each of the following situations, statewhether you’d use a chi-square goodness-of-fit test,a chi-square test of homogeneity, a chi-square test ofindependence, or some other statistical test:
a) A brokerage firm wants to see whether the type ofaccount a customer has (Silver, Gold, or Platinum)affects the type of trades that customer makes (in per-son, by phone, or on the Internet). It collects a randomsample of trades made for its customers over the pastyear and performs a test.
b) That brokerage firm also wants to know if the type ofaccount affects the size of the account (in dollars). Itperforms a test to see if the mean size of the account isthe same for the three account types.
c) The academic research office at a large communitycollege wants to see whether the distribution ofcourses chosen (Humanities, Social Science, orScience) is different for its residential and nonresi-dential students. It assembles last semester’s data andperforms a test.

You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: ${\displaystyle H_0}$: pA=0.3,pB=0.1; pC=0.1; pD=0.5
Complete the table. Report all answers accurate to three decimal places.
$\begin{array}{|ccc|}\hline \text{ Category }& \text{ Observed Frequency }& \text{ Expected Frequency }\\ \text{ A }& 24\\ \text{ B }& 12\\ \text{ C }& 7\\ \text{ D }& 44\\ \hline\end{array}$
What is the chi-square test-statistic for this data?
${\displaystyle {\chi }^2=}$
What is the P-Value?
P-Value=

You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.
$\begin{array}{|ccc|}\hline \text{ Category }& \text{ Population \#1 }& \text{ Population \#2 }\\ \text{ A }& 11& 14\\ \text{ B }& 56& 105\\ \hline\end{array}$
What is the chi-square test-statistic for this data?
${\displaystyle {\chi }^2=}$
Report all answers accurate to three decimal places.

You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.
$\begin{array}{|ccc|}\hline \text{ Category }& \text{ Population \#1 }& \text{ Population \#2 }\\ \text{ A }& 36& 125\\ \text{ B }& 22& 68\\ \hline\end{array}$
What is the chi-square test-statistic for this data?
${\displaystyle {\chi }^2=}$
Report all answers accurate to three decimal places.

You are conducting a multinomial hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table.
$\begin{array}{|cccc|}\hline \text{ Category }& \text{ Observed Frequency }& \text{ Expected Frequency }& \text{ Squared Pearson Residual }\\ \text{ A }& 18\\ \text{ B }& 10\\ \text{ C }& 15\\ \text{ D }& 17\\ \text{ E }& 17\\ \hline\end{array}$
What is the chi-square test-statistic for this data?
${\displaystyle {\chi }^2=}$
Report all answers accurate to three decimal places.