Exam 12: Tests of Goodness of Fit, Independence and Multiple Proportions

One thousand managers with degrees in business administration indicated their fields of concentration as shown below. Test at $\alpha$ = .01 to determine if the position in management is independent of the major of concentration.

In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be

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 hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

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

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. -Excel's ____ function is used to perform a test of independence.

Exhibit 12-6 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. -Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major: Has there been any significant change in the number of students in each major between the last school year and this school year? Use $\alpha$ = 0.05.

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

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 hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

Members of a focus group stated their preferences between three possible slogans. The results follow. Use Excel to test at $\alpha$ = .05 to determine any difference in preference among the three slogans.

A goodness of fit test is always conducted as 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

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 test statistic is

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. -In a goodness of fit test, Excel's CHISQ.DIST.RT function returns a

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. -Excel's CHISQ.DIST function can be used to perform

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

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, test to determine if the type of car purchased is independent of the city in which the purchasers live.

A group of 500 individuals were asked to cast their votes regarding a particular issue of the Equal Rights Amendment. The following contingency table shows the results of the votes: Test at $\alpha$ = .05 to determine if the votes cast were independent of the gender of the individuals.

Exhibit 12-6 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. -Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With $\alpha$ = 0.05, test to see if the methods of payment have changed during the Christmas rush.

Exhibit 12-6 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. -In the last presidential election before the candidates began their major campaigns, the percentages of registered voters who favored the various candidates were as follows: After the major campaigns began, a random sample of 400 voters showed that 172 favored the Republican candidate; 164 were in favor of the Democratic candidate; and 64 favored the Independent candidate. Test with $\alpha$ = .01 to see if the proportion of voters who favored the various candidates changed.

A sample of 150 individuals (males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. The results of the survey are shown below. Test at $\alpha$ = 0.05 to determine if the yearly income is independent of the gender.