Exam 12: Tests of Goodness of Fit and Independence

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 calculated value for the test statistic 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?

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 $\alpha$ = .05.

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 expected number of adults who prefer coffee is

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

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 number of degrees of freedom associated with this problem is

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

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 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 calculated value for the test statistic equals

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.At 95% confidence,the null hypothesis

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 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.At 95% confidence,the conclusion of the test is that 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.The calculated value for the test statistic equals

The degrees of freedom for a contingency table with 10 rows and 11 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 12-4 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

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

A medical journal reported the following frequencies of deaths due to cardiac arrest for each day of the week: 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.

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 expected frequency for each group 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 conclusion of the test is that the