Exam 12: Tests of Goodness of Fit and Independence

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 12-1 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 number of degrees of freedom associated with this problem is

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

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.This problem is an example of a

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

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.

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

Dr.Sherri Brock's 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.

The number of emergency calls per day at a hospital over a period of 120 days is shown below. Use $\alpha$ = 0.05 and the p-value approach to see if the above data have a Poisson distribution.

Exhibit 12-8 The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. -Refer to Exhibit 12-8.The calculated value for the test statistic equals

The following table shows the results of recent study regarding gender of individuals and their selected field of study. We want to determine if the selected field of study is independent of gender. a.Compute the test statistic. b.Using the p-value approach at 90% confidence,test to see if the field of study is independent of gender. c.Using the critical method approach at 90% confidence,test for the independence of major and gender.

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 number of freshmen is

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

A group of 2000 individuals from 3 different cities were asked whether they owned a foreign or a domestic car.The following contingency table shows the results of the survey. At $\alpha$ = 0.05 using the p-value approach,test to determine if the type of car purchased is independent of the city in which the purchasers live.

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 calculated value for the test statistic equals

Before the presidential debates,it was expected that the percentages of registered voters in favor of various candidates would be as follows. After the presidential debates,a random sample of 1200 voters showed that 540 favored the Democratic candidate;480 were in favor of the Republican candidate;40 were in favor of the Independent candidate,and 140 were undecided.We want to see if the proportion of voters has changed. a.Compute the test statistic. b.Use the p-value approach to test the hypotheses.Let $\alpha$ = .05. c.Using the critical value approach,test the hypotheses.Let $\alpha$ = .05.

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

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is

An important application of the chi-square distribution is