Exam 12: Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. -Refer to Exhibit 12-4. The expected frequency for the Business College is

The degrees of freedom for a contingency table with 12 rows and 12 columns is

Exhibit 12-1 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. -Refer to Exhibit 12-1. The p-value is

Exhibit 12-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. -Refer to Exhibit 12-2. The expected frequency of seniors is

A population where each element of the population is assigned to one and only one of several classes or categories is a

Shown below is 3 x 2 contingency table with observed values from a sample of 1,500. At 95% confidence, test for independence of the row and column factors.

Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration. We want to determine if the position in management is independent of field (major) of concentration. a.Compute the test statistic. b.Using the p-value approach at 90% confidence, test to determine if management position is independent of major. c.Using the critical value approach, test the hypotheses. Let $\alpha$ = 0.10.

The sampling distribution for a goodness of fit test is the

Exhibit 12-6 The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies: -Refer to Exhibit 12-6. At 95% confidence, the conclusion of the test is that the

Testing the equality of three or more population proportions

Exhibit 12-3 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. We are interested in determining whether or not the medication was effective in curing the common cold. -Refer to Exhibit 12-3. The p-value is

Exhibit 12-6 The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies: -Refer to Exhibit 12-6. The p-value is

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. -Refer to Exhibit 12-4. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

A professor believes that the final examination scores in statistics are normally distributed. A sample of 40 final scores has been taken. You are given the sample below. The mean of the scores is 83.1, and the standard deviation is 10.43. a.State the null and alternative hypotheses. b.Compute the test statistic for the goodness of fit test. c.At 99% confidence using the p-value approach, test the hypotheses. What do you conclude about the distribution of final examination scores?

Dr. Maria Pecora diet pills are supposed to cause significant weight loss. The following table shows the results of a recent study where some individuals took the diet pills and some did not. We want to see if losing weight is independent of taking the diet pills. a.Compute the test statistic. b.Using the p-value approach at 95% confidence, test to determine if weight loss is independent on taking the pill. c.Use the critical method approach and test for independence.

Exhibit 12-6 The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies: -Refer to Exhibit 12-6. The expected frequency of exactly 3 cars arriving in a 10-minute interval is

Exhibit 12-7 You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83, and the standard deviation equals 4.53. -Refer to Exhibit 12-7. The expected frequency in the 3rd interval is

Marascuillo procedure is used for testing the equality of three or more population

In 2002, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2003, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see if there has been a significant change in the proportions between 2002 and 2003.

Exhibit 12-5 The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences. -Refer to Exhibit 12-5. The p-value is