Question 1

Which of the following should be used if we want to conduct a two-tail test of a population proportion?
A)z-test of a population proportion.
B)Chi-squared test of a binomial experiment since $z ^ { 2 } = \chi ^ { 2 }$ .
C)the chi-squared test of a contingency table.
D)z-test of a population proportion and Chi-squared test of a binomial experiment since $z ^ { 2 } = \chi ^ { 2 }$ .
E)Chi-squared test of a binomial experiment since $z ^ { 2 } = \chi ^ { 2 }$ and the chi-squared test of a contingency table.

Accepted Answer

A z-test of a population proportion is appropriate for testing hypotheses about a population proportion in a two-tailed test. Additionally, the chi-squared test of a binomial experiment can also be used because the square of a z-score is equivalent to a chi-squared value with one degree of freedom, making both A and B correct. Therefore, D, which includes both options, is the correct answer.

Question 2

If each element in a population is classified into one and only one of several categories, the population is a:
A)normal population.
B)multinomial population.
C)chi-squared population.
D)binomial population.

Accepted Answer

If each element in a population is classified into one and only one of several categories, the population is a multinomial population. This is because the variable being studied has multiple possible outcomes (categories) and each observation falls into one of these categories.

Question 3

Which of the following best describes the degrees of freedom needed in a Chi-squared test for normality?
A)Number of intervals used to test the hypothesis minus 1.
B)Number of parameters estimated minus 1.
C)Number of intervals used to test the hypothesis minus the number of parameters estimated minus 1.
D)Number of intervals used to test the hypothesis minus the number of parameters estimated minus 2.

Accepted Answer

The degrees of freedom for a Chi-squared test for normality are calculated as df = k - p - 1, where k is the number of intervals used to test the hypothesis and p is the number of parameters estimated. This formula accounts for the fact that the intervals must be independent of each other, and that the estimated parameters reduce the amount of variability in the data. Therefore, the correct answer is C.

Question 4

The vice-chancellor of a university collected data from students concerning the building of a new library, and classified the responses into different categories (strongly agree, agree, undecided, disagree, strongly disagree) and according to whether the student was male or female. Which of the following tests should be used to test whether responses and gender are independent?
A)Chi-squared test for goodness-of-fit.
B)Chi-squared test for normality.
C)Chi-square test of a multinomial experiment.
D)Chi-squared test of a contingency table.

Accepted Answer

A chi-squared test of a contingency table is used to determine if there is a relationship between two categorical variables, in this case, responses and gender. This test compares the observed frequencies in each category to the expected frequencies if the categories were independent. Therefore, this is the best choice for testing whether the responses and gender are independent.

Question 5

Which of the following may be used to determine whether data were drawn a particular distribution?
A)Chi-squared goodness-of-fit test.
B)Chi-squared test of a contingency table.
C)Z test.
D)All of these choices are correct.

Accepted Answer

The chi-squared goodness-of-fit test is specifically designed to determine whether a set of data comes from a particular distribution. The other tests listed are not typically used for this purpose.

Question 6

To determine the critical values in the chi-squared distribution table, the process requires which of the following information?
A)Degrees of freedom.
B)Probability of Type I error.
C)Probability of Type II error.
D)Degrees of freedom and Probability of Type I error.

Accepted Answer

To determine the critical values in the chi-squared distribution table, both the degrees of freedom (which depend on the number of categories or groups in the data) and the probability of Type I error (the significance level, often denoted as alpha, which is the probability of rejecting the null hypothesis when it is true) are required. The probability of Type II error is not directly used in finding critical values in this context.

Question 7

Which of the following best describes the number of degrees of freedom used in a Chi-squared test of independence if there is a contingency table with 5 rows and 3 columns?
A)7
B)8
C)15
D)10

Accepted Answer

The answer of Which of the following best describes the...

Question 8

Which of the following are the degrees of freedom used in a Chi-squared test of independence between gender and mode of transport to university, if the mode of transport choices are public transport, car, bicycle or other.
A)8
B)5
C)4
D)3

Accepted Answer

The degrees of freedom for a Chi-squared test of independence are calculated as (r - 1) * (c - 1), where r is the number of rows and c is the number of columns in the contingency table. Here, gender has 2 categories (male and female) and mode of transport has 4 categories (public transport, car, bicycle, other), making the table 2x4. Thus, degrees of freedom = (2-1) * (4-1) = 1 * 3 = 3.

Question 9

Of the values for a chi-squared test statistic listed below, which one is likely to lead to rejection of the null hypothesis in a goodness-of-fit test?
A)0.
B)1.
C)2.
D)40.

Accepted Answer

A larger chi-squared test statistic indicates a larger deviation between observed and expected values, which would suggest a poor fit to the null hypothesis. Therefore, a larger value such as 40 is more likely to lead to rejection of the null hypothesis in a goodness-of-fit test.

Question 10

Which of the following best describes the approach taken if the expected frequency $e _ { i }$ for any cell i is less than 5?
A)We must choose another sample of five or more observations.
B)We should use the normal distribution instead of the chi-squared distribution.
C)We should combine the cells such that each observed frequency $f _ { i }$ is 5 or more.
D)We must increase the number of degrees of freedom for the test by 5.

Accepted Answer

When the expected frequency $e _ { i }$ for any cell i is less than 5, the appropriate approach is to combine cells to ensure that each expected frequency is 5 or more. This is done to meet the assumptions of the chi-squared test, which requires sufficient expected frequencies in each category for the approximation to the chi-squared distribution to be valid.

Question 11

Which of the following uses the Chi-square distribution?
A)Test of independence between two categorical variables.
B)Test of a multinomial experiment with one categorical variable.
C)Test about a single population variance with one numerical variable.
D)All of these choices are correct.

Accepted Answer

All of these choices correctly describe situations where the Chi-square distribution is used: A) for testing independence between two categorical variables, B) in the context of a multinomial experiment involving one categorical variable, and C) when testing hypotheses about a single population variance, which involves one numerical variable.

Question 12

A chi-squared test of a contingency table with 4 rows and 4 columns shows that the value of the test statistic is 23. Which of the following best describes the p-value for this test?
A)p-value < 0.010
B)p-value < 0.005
C)p-value > 0.10
D)0.005 < p-value < 0.01

Accepted Answer

The answer of A chi-squared test of a contingency table...

Question 13

Which of the following uses a contingency table?
A)Chi-squared test of independence of two numerical variables in a population.
B)Chi-squared test of independence of two nominal variables in a sample.
C)Chi-squared test of independence of two numerical variables in a sample.
D)Chi-squared test of independence of two nominal variables in a population.

Accepted Answer

The answer of Which of the following uses a contingency...

Question 14

Which statistical technique is appropriate when we describe a single population of nominal data with exactly two categories?
A)z-test of a population proportion.
B)Chi-squared test of a multinomial experiment.
C)Chi-squared test of a contingency table.
D)z-test of a population proportion and Chi-squared test of a multinomial experiment.
E)Chi-squared test of a multinomial experiment and Chi-squared test of a contingency table.

Accepted Answer

The answer of Which statistical technique is appropriate when we...

Question 15

Which of the following would be used to analyse the relationship between two categorical variables?
A)Z-test of a population proportion.
B)Chi-squared test of a binomial experiment since $z ^ { 2 } = \chi ^ { 2 }$ .
C)A Chi-squared test of a binomial experiment or a Chi-squared test of a contingency table.
D)Chi-squared test of a contingency table.
E)None of these choices are correct.

Accepted Answer

A Chi-squared test of a contingency table is used to analyze the relationship between two categorical variables.

Question 16

Which of the following best describes a Chi-squared goodness-of-fit test?
A)Two tailed test
B)Left tailed test
C)Right tailed test
D)All of these choices are correct.

Accepted Answer

A Chi-squared goodness-of-fit test is a right-tailed test because it tests whether the observed frequencies differ from the expected frequencies, with the test statistic being large when there is a significant difference.

Question 17

Which statistical technique is appropriate when we wish to analyse the relationship between two nominal variables with two or more categories?
A)Chi-squared test of a multinomial experiment.
B)Chi-squared test of a contingency table.
C)t-test of the difference between two means.
D)Z-test of the difference of two means
E)F-test of analysis of variance

Accepted Answer

The chi-squared test of a contingency table is appropriate when we wish to analyse the relationship between two nominal variables with two or more categories. It allows us to determine whether there is a statistically significant association between the variables.

Question 18

Which of the following may be used for hypothesis tests of nominal (categorical) data?
A)Chi-squared test of a multinomial experiment.
B)Z test of a population proportion or a Z test for the difference between two population proportions.
C)Chi-squared test of a contingency table.
D)All of these choices are correct.

Accepted Answer

All of these choices are appropriate for hypothesis testing of nominal data. Chi-squared tests are commonly used for analyzing categorical data, including contingency tables and multinomial experiments. Z-tests can also be used for comparing two proportions, but are limited to binary data.

Question 19

Which of the following is the correct decision in a goodness-of-fit test, if the calculated value of the test statistic is 20.08 and there are 10 categories, testing at 1% level of significance?
A)We reject Ho because p-value < 0.01.
B)We do not reject Ho because p-value < 0.01.
C)We reject Ho because 0.01 < p-value < 0.025.
D)We do not reject Ho because 0.01 < p-value < 0.025.

Accepted Answer

The answer of Which of the following is the correct...

Question 20

In a goodness-of-fit test, suppose that a sample showed that the observed frequency $f _ { i }$ and expected frequency $e _ { i }$ were equal for each cell i. Which of the following best describes the decision for the hypothesis test?
A)Reject Ho at $\alpha$ of 0.05 but do not reject Ho at $\alpha$of 0.025.
B)Reject Ho at any level of $\alpha$.
C)Do not reject Ho at any level of $\alpha$.
D)Do not reject Ho at $\alpha$ of 0.05 but reject Ho at $\alpha$ of 0.025.

Accepted Answer

When the observed frequencies $f_i$ match the expected frequencies $e_i$ for each cell, it indicates a perfect fit between the observed data and the expected distribution under the null hypothesis $H_0$. This scenario would result in a chi-square statistic of 0, leading to a p-value greater than any conventional alpha level ($\alpha$), thus we would not reject $H_0$ at any level of $\alpha$.

Quiz 14: Additional Tests for Nominal Data: Chi-Squared Tests

Which of the following should be used if we want to conduct a two-tail test of a population proportion?

If each element in a population is classified into one and only one of several categories, the population is a:

Which of the following best describes the degrees of freedom needed in a Chi-squared test for normality?

Which of the following may be used to determine whether data were drawn a particular distribution?

To determine the critical values in the chi-squared distribution table, the process requires which of the following information?

Which of the following best describes the number of degrees of freedom used in a Chi-squared test of independence if there is a contingency table with 5 rows and 3 columns?

Which of the following are the degrees of freedom used in a Chi-squared test of independence between gender and mode of transport to university, if the mode of transport choices are public transport, car, bicycle or other.

Of the values for a chi-squared test statistic listed below, which one is likely to lead to rejection of the null hypothesis in a goodness-of-fit test?

Which of the following best describes the approach taken if the expected frequency eie _ { i }ei​ for any cell i is less than 5?

Which of the following uses the Chi-square distribution?

A chi-squared test of a contingency table with 4 rows and 4 columns shows that the value of the test statistic is 23. Which of the following best describes the p-value for this test?

Which of the following uses a contingency table?

Which statistical technique is appropriate when we describe a single population of nominal data with exactly two categories?

Which of the following would be used to analyse the relationship between two categorical variables?

Which of the following best describes a Chi-squared goodness-of-fit test?

Which statistical technique is appropriate when we wish to analyse the relationship between two nominal variables with two or more categories?

Which of the following may be used for hypothesis tests of nominal (categorical) data?

Which of the following is the correct decision in a goodness-of-fit test, if the calculated value of the test statistic is 20.08 and there are 10 categories, testing at 1% level of significance?

In a goodness-of-fit test, suppose that a sample showed that the observed frequency fif _ { i }fi​ and expected frequency eie _ { i }ei​ were equal for each cell i. Which of the following best describes the decision for the hypothesis test?

Which of the following best describes the approach taken if the expected frequency $e _ { i }$ for any cell i is less than 5?

In a goodness-of-fit test, suppose that a sample showed that the observed frequency $f _ { i }$ and expected frequency $e _ { i }$ were equal for each cell i. Which of the following best describes the decision for the hypothesis test?