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

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

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?

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

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

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. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Issues }$ Plant Location Very interesting Fairly interesting Not interesting Melbourne 60 62 78 Adelaide 70 56 74 Do the data indicate at the 5% significance level that there are differences between the two plants regarding which issue should be the primary one?

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 Compute the value of the test statistic.

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

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?

A sport preference poll showed the following data for men and women: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Favourite Sport }$ Gender Rugby Basketball Football Golf Tennis Male 24 17 30 18 22 Female 21 20 22 12 28 Using the 5% level of significance, test to determine whether sport preferences depend on gender.

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