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

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.

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

A salesperson makes five calls per day. A sample of 200 days gives the frequencies of 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. Compute the expected frequencies for x = 0, 1, 2, 3, 4 and 5 by using the binomial probability function or the binomial tables. Combine categories if necessary to satisfy the rule of five.

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.

In 2003, the student body of a University in NSW consisted of 30% first-years, 25% second-years, 27% third-years, and 18% fourth-years. A sample of 400 students taken from the 2004 student body showed that there are 138 first-years, 88 second-years, 94 third-years, and 80 fourth-years. Test with 5% significance level to determine whether the student body proportions have changed.

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 Can you infer at the 5% significance level that the proportional support by the Adelaide employees for the three issues has changed since the pamphlet was circulated?

Explain what is meant by the rule of five.

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

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. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Response }$ Gender Very interesting Fairly interesting Not interesting Male 70 41 9 Female 35 34 11 Do the data provide sufficient evidence to conclude that the level of job satisfaction is related to gender? Use $\alpha =$ 0.10.

A biology professor claimed that the proportions of grades in his classes are the same Grade A B C D F Frequency 14 23 27 26 10 State the null and alternative hypotheses to be tested.

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 to determine whether data were drawn a particular distribution?

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

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

A telephone company prepared four versions of a set of instructions for placing collect calls. The company asked a sample of 1600 people which one of the four forms was easiest to understand. In the sample, 425 people preferred Form A, 385 preferred Form B, 375 preferred Form C, and 415 preferred Form D. At the 5% level of significance, can one conclude that in the population there is a preferred form?

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

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

Consider a multinomial experiment involving 160 trials and 4 categories (cells). The observed frequencies resulting from the experiment are shown in the following table. Category 1 2 3 4 Frequency 53 35 30 42 Use the 10% significance level to test the hypotheses. $H _ { 0 } : p _ { 1 } = p _ { 2 } = p _ { 3 } = p _ { 4 }$ . $H _ { 1 } :$ At least two proportions differ from their specified values.

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

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