Exam 14: Analysis of Categorical Data

Business Decision Narrative The owner of Fit Forever Health Club is considering adding an indoor swimming pool to his facility. The manager decided to take a survey to determine whether member opinion about the addition of a pool was independent of the age of the member. Two hundred members were selected at random and asked to state their opinion. The following data were recorded: Opinion Concerning Pool Use the following output generated by statistical software to answer the questions below. Chi-Square Test Expected counts are printed below observed counts Chi-Sq = 2.482 + 0.604 + 1.091 + 0.000 + 0.197 + 0.204 + 4.119 + 0.193 +3.672 = 12.562 DF = 4, P-Value = 0.014 -Refer to Business Decision Narrative. What is the value of the test statistic?

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

Historically, a bank has employed 50% permanent full-time workers, 25% permanent part-time workers, 15% temporary full-time workers, and 10% temporary part-time workers. In a recent sample of 400 workers, 190 were permanent full-time, 125 were permanent part-time, 55 were temporary full-time, and 30 were temporary part-time. Use these data and $\alpha$ = 0.05 to assess whether there has been a change from the historical percentages.

Researchers from Germany claimed that the risk of a heart attack for a working person may be as much as 50% greater on Monday than on any other day. In an attempt to verify their claim, they surveyed 420 working people who had recently had heart attacks and recorded the day on which their heart attacks occurred: Do the data present sufficient evidence to indicate that there is a difference in the incidence of heart attacks depending on the day of the week? Test using = 0.05.

To be valid, a chi-square test of independence requires that the expected frequency for each cell in the contingency table equals ten or more.

Which of the following is our best option if the expected frequency for any cell i is less than five and we want to use Pearson's chi-square statistic in our experiment?

Ink Pen Colours Narrative A national survey stated that 30% of the population prefer to use a pen with black ink, 30% prefer blue ink, 25% prefer red ink, and 15% prefer some other colour. A statistics professor took a random sample of 80 students and asked them to state their ink colour preference. The following data was recorded: -Refer to Ink Pen Colours Narrative. State the null and alternative hypotheses to test whether the data agree with the percentages stated in the national survey.

What is the appropriate test to use if we wish to determine whether there is evidence that the proportion of successes is the same in group 1 as in group 2?

Consider a multinomial experiment with 200 trials, and the outcome of each trial can be classified into one of five categories. In this case, how many degrees of freedom would be associated with the chi-square goodness-of-fit test?

Which of the following statements is NOT a characteristic of a goodness-of-fit test?

In a chi-square goodness-of-fit test with 5 degrees of freedom and a significance level of 0.05, the chi-square value from the table is 11.0705. Which of the following computed values of the chi-square test statistic will lead to rejection of the null hypothesis?

If we wanted to conduct a two-tailed test of a population proportion, which of these tests could we employ?

Preferred Television Drama Narrative A pollster was interested in determining whether three television dramas are equally preferred by men and women. The following data were recorded: Preference -Refer to Preferred Television Drama Narrative. Compute the value of the test statistic.

Ink Pen Colours Narrative A national survey stated that 30% of the population prefer to use a pen with black ink, 30% prefer blue ink, 25% prefer red ink, and 15% prefer some other colour. A statistics professor took a random sample of 80 students and asked them to state their ink colour preference. The following data was recorded: -Refer to Ink Pen Colours Narrative. Compute the value of the test statistic.

Chi-square tests of independence are always lower-tailed because a perfect fit between and makes the test statistic equal to 0.

If each element in a population is classified into one and only one of several categories, which of the following best describes this kind of population?

A chi-square test for independence is applied to a contingency table with three rows and five columns for two qualitative variables. The degrees of freedom for this test is 8.

The area to the right of a chi-square value is 0.01. For 8 degrees of freedom, the table value is 1.64648.

Average Casino Dice Rolls Narrative A casino customer is concerned about whether the dice the casino is using are "fair" (i.e., each face is equally likely to appear). The customer obtains a die that is being used by the casino and rolls it 240 times. The customer records the following data: -Refer to Average Casino Dice Rolls Narrative. Compute the value of the test statistic.

Which of the following statements is NOT a property of a contingency table test?