Exam 11: Comparisons Involving Proportions and a Test of Independence

Both the hypothesis test for proportions of a multinomial population and the test of independence employ the

A lottery is conducted that involves the random selection of numbers from 0 to 4. To make sure that the lottery is fair, a sample of 250 was taken. The following results were obtained. 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 5% level of significance. Determine the critical value from the table. d.What do you conclude about the fairness of this lottery?

Exhibit 11-5 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 11-5. The calculated value for the test statistic equals

Exhibit 11-4 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 11-4. The conclusion of the test (at 95% confidence) is that the

Exhibit 11-1 The results of a recent poll on the preference of shoppers regarding two products are shown below. -Refer to Exhibit 11-1. The standard error of is

An important application of the chi-square distribution is

In 2009, 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 2010, 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 whether there has been a significant change in the proportions between 2009 and 2010.

A goodness of fit test is always conducted as a

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 11-6 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 11-6. The p-value is

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   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.

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

Exhibit 11-2 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. -Refer to Exhibit 11-2. The p-value is

Two hundred fifty managers with degrees in business administration indicated their fields of concentration as shown below. At   .01 using the p-value approach, test to determine if the position in management is independent of the major of concentration.

A comparative study of organic and conventionally grown produce checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. Coli in organic versus conventionally grown produce? Test at   0.10.

The personnel department of a large corporation reported sixty resignations during the last year. The following table groups these resignations according to the season in which they occurred. Test to see if the number of resignations is uniform over the four seasons. Let   0.05.

Exhibit 11-8 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 11-8. With a .05 level of significance, the critical value for the test is

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: We want to see if there has been a significant change in the number of students in each major. a.Compute the test statistic. b.Has there been any significant change in the number of students in each major between the last school year and this school year. Use the p-value approach and let   .05.

Exhibit 11-3 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. -Refer to Exhibit 11-3. The point estimate for the difference between the proportions is

If the p-value is less than ,