Exam 11: Comparisons Involving Proportions and a Test of Independence

Exhibit 11-4 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 11-4. This problem is an example of a

A medical journal reported the following frequencies of deaths due to cardiac arrest for each day of the week: Cardiac Death by Day of the Week Day f Monday 40 Tuesday 17 Wednesday 16 Thursday 29 Friday 15 Saturday 20 Sunday 17 We want to determine whether the number of deaths is uniform over the week. a. Compute the test statistic. b. Using the p-value approach at 95% confidence, test for the uniformity of death over the week. c. Using the critical value approach, perform the test for uniformity.

Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration. Major Top Management Middle Management TOTAL Management 280 220 500 Marketing 120 80 200 Accounting 150 150 300 TOTAI 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 ? = 0.10.

A sample of 150 individuals males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. Their incomes were categorized as follows. Category 1 \ 20,000 upto \ 40,000 Category 2 \ 40,000 upto \ 60,000 Category 3 \ 60,000 upto \ 80,000 The results of the survey are shown below. Income Category Male Famale Category 1 10 30 Category 2 35 15 Category 3 15 45 We want to determine if yearly income is independent of gender. a. Compute the test statistic. b. Using the p-value approach, test to determine if yearly income is independent of gender.

In the last presidential election, before the candidates started their major campaigns, the percentages of registered voters who favored the various candidates were as follows. Percentages Republicans 34\% Democrats 43\% Independents 23\% 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. We are interested in determining whether the proportion of voters who favored the various candidates had changed. a. Compute the test statistic. b. Using the p-value approach, test to see if the proportions have changed. c. Using the critical value approach, test the hypotheses.

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

Exhibit 11-6 The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. Political Party Support Democrats 100 Republicans 120 Independents 80 We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. -Refer to Exhibit 11-6. The number of degrees of freedom associated with this problem is

Exhibit 11-9 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Teenagers Favoring Music Type Teenagers Surveyed This Type Pop 800 384 Rap 900 450 -Refer to Exhibit 11-9. The point estimate for the difference between the proportions is

Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president. a. Compute the test statistic. b. At alpha = .05, test to see if there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. Use the p-value approach.)

The makers of Compute-All know that in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old. a. State the null and alternative hypotheses to be tested. b. Compute the test statistic. c. The null hypothesis is to be tested at the 1% level of significance. Determine the critical value from the table. d. What do you conclude?

In a sample of 700 Republicans, 644 were opposed to the President's foreign policies. While in a sample of 600 Democrats, 528 were opposed to his policies. Develop a 95% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

During the primary elections of 1996, candidate A showed the following pre-election voter support in Tennessee and Mississippi. Voters Surveyed Voters Favoring Candidate A Tennessee 500 295 Mississippi 700 357 a. Develop a 95% confidence interval estimate for the difference between the proportion of voters favoring candidate A in the two states. b. Is there conclusive evidence that one of the two states had a larger proportion of voters' support? If yes, which state? Explain.

Before the start of the Winter Olympics, it was expected that the percentages of medals awarded to the top contenders to be as follows. Percentages United States 25\% Germany 22\% Norway 18\% Austria 14\% Russia 11\% France 10\% Midway through the Olympics, of the 120 medals awarded, the following distribution was observed. Number of Medals United States 33 Germany 36 Norway 18 Austria 15 Russia 12 France 6 We want to test to see if there is a significant difference between the expected and actual awards given. a. Compute the test statistic. b. Using the p-value approach, test to see if there is a significant difference between the expected and the actual values. Let α = .05. c. At 95% confidence, test for a significant difference using the critical value approach.

Exhibit 11-2 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. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 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 11-2. The expected frequency of seniors is

From production line A, a sample of 500 items is selected at random, and it is determined that 30 items are defective. In a sample of 300 items from production process B which produces identical items to line A), there are 12 defective items. Determine a 95% confidence interval estimate for the difference between the proportion of defectives in the two lines.

Prior to the start of the season, it was expected that audience proportions for the four major news networks would be CBS 18.6%, NBC 12.5%, ABC 28.9% and BBC 40%. A recent sample of homes yielded the following viewing audience data. Observed frequenciesf CBS 400 NBC 230 560 810 Total 2000 We want to determine whether or not the recent sample supports the expectations for the number of homes of the viewing audience of the four networks. a. State the null and alternative hypotheses to be tested. b. Compute the test statistic. c. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. d. What do you conclude?

Of 200 UTC seniors surveyed, 60 were planning on attending Graduate School. At UTK, 400 seniors were surveyed and 100 indicated that they were planning to attend Graduate School. a. Determine a 95% confidence interval estimate for the difference between the proportion of seniors at the two universities that were planning to attend Graduate School. b. Is there conclusive evidence to prove that the proportion of students from UTC who plan to go to Graduate School is significantly more than those from UTK? Explain.

The degrees of freedom for a contingency table with 10 rows and 11 columns is

Exhibit 11-9 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Teenagers Favoring Music Type Teenagers Surveyed This Type Pop 800 384 Rap 900 450 -For a two-tailed test at 98.5% confidence, Z =

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. Type of Car Detroit Atlanta Denver Total Domestic 80 200 520 800 Foreign 120 600 480 1200 Total 200 800 1000 2000 At α = 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.