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

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.

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

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

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

A major insurance firm interviewed a random sample of 1500 college students to find out the type of life insurance preferred, if any. The results follow: Insurance Preference Gender Term Whole life No insurance Female 170 110 470 Male 195 75 480 Is there evidence that the life insurance preference of male students is different to that of female students? Test using the 5% level of significance.

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

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 $x ^ { 2 }$ -statistic.)

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

Which of the following uses the Chi-square distribution?

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:

A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies. Grade A B C D F Frequency 14 23 27 26 10 Determine the rejection region at the 5% significance level.

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.

An Australian tyre manufacturer operates a plant in Melbourne and another plant in Adelaide. Employees at each plant have been evenly divided among three issues (wages, working conditions and super benefits) in terms of which one they feel should be the primary issue in the upcoming contract negotiations. The secretary of the union has recently circulated pamphlets among the employees, attempting to convince them that super benefits should be the primary issue. A subsequent survey revealed the following breakdown of the employees according to the plant at which they worked and the issue that they felt should be supported as the primary one. Issues Plant Location Very interesting Fairly interesting Not interesting Mel bourne 60 62 78 Adelaide 70 56 74 Can you infer at the 5% significance level that the proportional support by the Melbourne employees for the three issues has changed since the pamphlet was circulated?

A chi-squared test for independence with 6 degrees of freedom results in a test statistic $\chi ^ { 2 } = 13.58$ . Using the $x ^ { 2 }$ tables, the most accurate statement that can be made about the p-value for this test is that:

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

A university lecturer had the following semester 1 student's final grades for the course that they teach: 8% High Distinction, 35% Distinction, 40% Credit, 12% Pass, and 5% Failed. A sample of 100 second semester final grades for the same course showed 12 High distinctions, 30 Distinctions, 35 Credits, 15 Passes, and 8 Fails. Test at the 10% significance level to determine whether the semester one grades differ significantly from the semester two grades.

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

A caterer proposes to serve four main courses. For planning purposes, the caterer expects that the proportions of each that will be selected by customers will be: Selection Proportion Roast beef 0.50 Chicken 0.20 Fish 0.10 Vegeterian 0.20 Of the first 100 customers, 44 select roast beef, 24 select chicken, 13 select fish, and 19 select the vegetarian meal. Should the caterer revise the estimates? Use $\alpha$ = 0.05.

An Australian tyre manufacturer operates a plant in Melbourne and another plant in Adelaide. Employees at each plant have been evenly divided among three issues (wages, working conditions and super benefits) in terms of which one they feel should be the primary issue in the upcoming contract negotiations. The secretary of the union has recently circulated pamphlets among the employees, attempting to convince them that super benefits should be the primary issue. A subsequent survey revealed the following breakdown of the employees according to the plant at which they worked and the issue that they felt should be supported as the primary one. Issues Plant Location Very interesting Fairly interesting Not interesting Mel bourne 60 62 78 Adelaide 70 56 74 Can you infer at the 5% significance level that the proportional support by the employees at both plants for the issues has changed since the pamphlet was circulated?