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

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 = 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.

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

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

A large carpet store wishes to determine if the brand of carpet purchased is related to the purchaser's family income. As a sampling frame, they mailed a survey to people who have a store credit card. Five hundred customers returned the survey and the results follow: Brand of Carpet Family Income Brand A Brand B Brand C High income 65 32 32 Middle income 80 68 104 Low income 25 35 59 At the 5% level of significance, can you conclude that the brand of carpet purchased is related to the purchaser's family income?

A coffee machine sales representative visits 5 businesses per day. A sample of 200 days gives the frequencies of coffee machine sales volumes listed below: Number of sales Observed frequency (days) 0 10 1 38 2 69 3 63 4 18 5 2 Assume that the population is binomially distributed with a probability of purchase p = 0.50. Should the assumption of a binomial distribution be rejected at the 1% significance level?

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.)

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 $p _ { 1 } - p _ { 2 }$ .

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

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

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

To determine whether a single coin is fair, the coin was tossed 200 times. The observed frequencies with which each of the two sides of the coin turned up are recorded as 112 heads and 88 tails. Is there sufficient evidence at the 5% significance level to allow you to conclude that the coin is not fair?

Explain what is meant by the rule of five.

The number of cars sold by three salespersons over a 3-month period are shown below: Brandof Car Salesperson Brand A Brand B Brand C David 7 2 6 Edward 11 4 8 Frank 8 5 3 Using the 5% level of significance, test for the independence of salesperson and type of product sold.

Which of the following statements is not correct? A. The chi-squared test of independence is a one-sample test. B. Both variables in the chi-squared test of independence are nominal variables. C. The chi-squared goodness-of-fit test involves two categorical variables. D. The chi-squared distribution is skewed to the right.

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.

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.

The president of a large university has been studying the relationship between male/female supervisory structures in his institution and the level of employees' job satisfaction. The results of a recent survey are shown in the table below. Conduct a test at the 5% significance level to determine whether the level of job satisfaction depends on the boss/employee gender relationship. Boss/Employee Level of Satisfaction Male/Female Female/Male Male/Male Female/Female Satisfied 60 15 50 15 Neutral 27 45 48 50 Dissatisfied 13 32 12 55

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.

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 Melbourne 60 62 78 Adel aide 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?

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.