Deck 17: Additional Tests for Nominal Data: Chi-Squared Tests

Question 1

Which of the following uses a contingency table?

Answer 1

D

Question 2

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

Answer 2

D

Question 3

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

Answer 3

C

Question 4

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

Question 5

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

Question 6

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

Question 7

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?

Question 8

Which of the following uses the Chi-square distribution?

Question 9

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

Question 10

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?

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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 α of 1%?

Question 16

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

Question 17

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?

Question 18

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?

Question 19

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

Question 20

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.

Question 21

Which statistical technique is appropriate when we compare two or more populations of nominal data with two or more categories?

Question 22

Which of the following statements is not correct? $\begin{array}{|l|l|}\hline \text { A. } & \text { The chi-squared distribution is symmetrical. } \\\hline \text { B. } & \text { The chi-squared distribution is skewed to the right. } \\\hline \text { C. } & \text { All values of the chi-squared distribution are positive. } \\\hline \text { D. } & \text { The critical region for a goodness-of-fit test with } k \text { categories is } \chi^{2}>\chi_{\alpha, k-1}^{2} . \\\hline\end{array}$

Question 23

Which of the following is not a characteristic of a multinomial experiment?

Question 24

Which of the following best describes the sampling distribution of the test statistic for a goodness-of-fit test with k categories?

Question 25

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

Question 26

A chi-squared test for independence with 6 degrees of freedom results in a test statistic . Using the tables, the most accurate statement that can be made about the p-value for this test is that:

Question 27

Which statistical technique is appropriate when we compare two populations of nominal data with exactly two categories?

Question 28

Which of the following statements is not correct?

Question 29

Which of the following tests do not use the Chi-squared distribution?

Question 30

The chi-squared test of a contingency table is based upon:

Question 31

The number of degrees of freedom in a test of a contingency table with 7 rows and 5 columns is:

Question 32

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population. The researcher estimated the population mean and population standard deviation from a sample of 500 observations. In addition, the researcher used 6 standardised intervals to test for normality. Using a 5% level of significance, the critical value for this test is:

Question 33

In chi-squared tests, the conventional and conservative rule - known as the rule of five - is to require that the:

Question 34

Consider a multinomial experiment with 100 trials, and the outcome of each trial can be classified into one of 4 categories. The number of degrees of freedom associated with the chi-squared goodness-of-fit test is:

Question 35

In a chi-squared test of a contingency table, the value of the test statistic was $\chi ^ { 2 } = 12.678$ , the significance level was $\alpha$ = 0.05 and the degrees of freedom was 6. Thus: A. we fail to reject the null hyp othesis at $\alpha = 0.05$ .
B. we reject the null hypothesis at $\alpha = 0.05$ .
C. we don't have enough evidence to accept or reject the null hypothesis at $\alpha = 0.05$ .
D. we should increase the level of significance in order to reject the null hypothesis.

Question 36

In a chi-squared goodness-of-fit test, if the expected frequencies $e _ { i }$ and the observed frequencies $f _ { i }$ were quite different, which of the following is the best conclusion? $\begin{array}{|l|l|}\hline \text { A. } & \text { Null hypothesis is false, and reject } \mathrm{H}_{O} \\\hline \text { B. } & \text { Null hypothesis is true, and retain } \mathrm{HO} . \\\hline \text { C. } & \text { Alternative hypothesis is false, reject } \mathrm{H}_{\mathrm{A}} \\\hline \text { D. } & \text { Chi-squared distribution is invalid, use } t \text {-distribution instead. } \\\hline\end{array}$

Question 37

Which of the following statements is true for the chi-squared tests? $\begin{array}{|l|l|}\hline \text { A. } & \text { Testing for equal proportions is identical to testing for goodness-of-fit. } \\\hline \text { B. } & \begin{array}{l}\text { The number of degrees of freedom in a test of a contingency table with } r \text { rows and } c \\\text { columns is }(r-1)(c-1) \text {. }\end{array} \\\hline \text { C. } & \text { The number of degrees of freedom in a goodness-of-fit test with } k \text { categories is } k-1 . \\\hline \text { D. } & \text { All of these choices are correct. } \\\hline\end{array}$

Question 38

Which of the following best describes the rejection region in a chi-squared test of independence?

Question 39

The degrees of freedom in a chi-squared test for normality, where the number of standardised intervals is 13 and there are 2 population parameters to be estimated from the data, is equal to:

Question 40

A left-tailed area in the chi-squared distribution equals 0.975. For df = 11, the table value equals:

Question 41

Whenever the expected frequency of a cell is less than 5, one remedy for this condition is to increase the size of the sample.

Question 42

For a chi-squared distributed random variable with 12 degrees of freedom and a level of significance of 0.05, the chi-squared value from the table is 21.0261. The computed value of the test statistics is 25.1687. This will lead us to reject the null hypothesis.

Question 43

The middle 0.95 portion of the chi-squared distribution with 9 degrees of freedom has table values of 3.32511 and 16.9190, respectively.

Question 44

A left-tailed area in the chi-squared distribution equals 0.10. For 5 degrees of freedom, the table value equals 9.23635.

Question 45

A left-tailed area in the chi-squared distribution equals 0.90. For 10 degrees of freedom, the table value equals 15.9871.

Question 46

In a chi-squared test of independence, the value of the test statistic was $\chi ^ { 2 } =$ 15.652, and the critical value at $\alpha = 0.025$ was 11.1433. Thus we must reject the null hypothesis at $\alpha = 0.025$ .

Question 47

A chi-squared goodness-of-fit test can be conducted either as a two-tail test or as a one-tail test.

Question 48

Whenever the expected frequency of a cell is less than 5, one possible remedy for this condition is to combine it with one or more other cells.

Question 49

A right-tailed area in the chi-squared distribution equals 0.01. For 4 degrees of freedom, the table value equals 13.2767.

Question 50

Whenever the expected frequency of a cell is less than 5, we must increase the significance level.

Question 51

A test for independence is applied to a contingency table with 4 rows and 4 columns for two nominal variables. The number of degrees of freedom for this test will be 9.

Question 52

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population. The researcher estimated the population mean and population standard deviation from a sample of 100 observations. In addition, the researcher used 6 standardised intervals to test for normality. Using a 2.5% level of significance, the critical value for this test is 9.3484.

Question 53

A Chi-squared test can be used to test the equality of two population means.

Question 54

One type of Chi-squared goodness of fit test is a Chi-squared test for normality.

Question 55

A test for independence is applied to a contingency table with 5 rows and 2 columns for two nominal variables. The number of degrees of freedom for this chi-squared test must be 4.

Question 56

The chi-squared test of independence is a Chi-squared test of a contingency table.

Question 57

A chi-squared test for independence with 6 degrees of freedom results in a test statistic of 13.25. Using the chi-squared table, the most accurate statement that can be made about the p-value for this test is that 0.025 < p-value < 0.05.

Question 58

A chi-squared test for independence with 10 degrees of freedom results in a test statistic of 17.894. Using the chi-squared table, the most accurate statement that can be made about the p-value for this test is that 0.05 < p-value < 0.10.

Question 59

For a chi-squared distributed random variable with 10 degrees of freedom and a level of significance of 0.025, the chi-squared value from the table is 20.5. The computed value of the test statistic is 16.857. The decision is to retain Ho.

Question 60

The null hypothesis states that the sample data came from a normally distributed population. The researcher calculates the sample mean and the sample standard deviation from the data. The data arrangement consisted of seven categories. Using a 0.05 significance level, the appropriate critical value for this chi-squared test for normality is 11.0705.

Question 61

In chi-squared tests, the conventional and conservative rule - known as the rule of five - is to require that difference between the observed and expected frequency for each cell be at least 5.

Question 62

An Australian firm has been accused of engaging in prejudicial hiring practices against women who have young children, where a young child is defined to be a child less than 12 years of age. According to the most recent census, the percentages of men, women without young children and women with young children in a certain community are 72%, 10% and 18%, respectively. A random sample of 200 employees of the firm revealed that 165 were men, 14 were women without young children and 21 were women with young children. Do the data provide sufficient evidence to conclude at the 10% level of significance that the firm has been engaged in prejudicial hiring practices?

Question 63

If we want to test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of $p _ { 1 } - p _ { 2 }$ , or the chi-squared test of a contingency table. (Squaring the value of the z-statistic yields the value of the $\chi ^ { 2 }$ -statistic.)

Question 64

The area to the right of a chi-squared value is 0.01. For 8 degrees of freedom, the table value is 20.0902.

Question 65

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of $p _ { 1 } - p _ { 2 }$ .

Question 66

The rule of five is used to ensure that the discrete distribution of the test statistic can be approximated by the continuous Chi-squared distribution.

Question 67

The number of degrees of freedom associated with the chi-squared test for normality is the number of intervals used minus the number of parameters estimated from the data.

Question 68

At present in Australia, voting in a Federal election is compulsory for all citizens 18 years or over.
There has been some discussion to have this changed from being compulsory to voluntary.
A study was done to investigate whether there was a relationship between gender and attitude towards changing voting in Australia from compulsory to voluntary. Participants were asked "Do you agree to change voting in Australian Federal Elections from compulsory to voluntary? A table of results from the sample is given below.
At the 1% level of significance, is there a relationship between gender and attitude towards voluntary voting?

Question 69

The personnel manager of a consumer product company asked a random sample of employees how they felt about the work they were doing. The following table gives a breakdown of their responses by gender. Do the data provide sufficient evidence to conclude that the level of job satisfaction is related to gender? Use 0.10.

Question 70

A sport preference poll showed the following data for men and women: Using the 5% level of significance, test to determine whether sport preferences depend on gender.

Question 71

The following data are believed to have come from a normal probability distribution.
The mean of this sample equals 26.80, and the standard deviation equals 6.378. Use the goodness-of-fit test at the 5% significance level to test this claim.

Question 72

Like that of the Student t-distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

Question 73

The number of degrees of freedom for a contingency table with r rows and c columns is (r -1)(c - 1), provided that both r and c follow the rule of five.

Question 74

When doing a Chi-squared goodness of fit test, we use Ho: The data are not normally distributed.

Question 75

If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of $p _ { 1 } - p _ { 2 }$ , or the chi-squared test of a contingency table. (Squaring the value of the z-statistic yields the value of the $\chi ^ { 2 }$ -statistic.)

Question 76

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population. The researcher estimated the population mean and population standard deviation from a sample of 200 observations. In addition, the researcher used 5 standardised intervals to test for normality. Using a 10% level of significance, the critical value for this test is 4.60517.

Question 77

The chi-squared goodness-of-fit test is usually used as a test of multinomial parameters, but it can also be used to determine whether data were drawn from any distribution.

Question 78

The chi-squared test of a contingency table is used to determine if there is enough evidence to infer that two nominal variables are related, and to infer that differences exist among two or more populations of nominal variables.

Question 79

A multinomial experiment, where the outcome of each trial can be classified into one of two categories, is identical to the binomial experiment.

Question 80

Five brands of orange juice are displayed side by side in several supermarkets in a large city. It was noted that in one day, 180 customers purchased orange juice. Of these, 30 picked Brand A, 40 picked Brand B, 25 picked Brand C, 35 picked Brand D, and 50 picked brand
E. In this city, can you conclude at the 5% significance level that there is a preferred brand of orange juice?