Exam 12: Tests of Goodness of Fit and Independence

The following data show the grades of a sample of 40 students who have taken statistics. Use $\alpha$ = 0.1 and conduct a goodness of fit test to determine if the sample comes from a population that has a normal distribution.Use the critical 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?

Five hundred randomly selected automobile owners were questioned on the main reason they had purchased their current automobile.The results are given below. a.State the null and alternative hypotheses for a contingency table test. b.State the decision rule for the critical value approach.Let $\alpha$ = .01. c.Calculate the $\chi$ ²test statistic. d.Give your conclusion for this test.

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 number of degrees of freedom associated with this problem is

Use $\alpha$ = 0.05 to determine if the following sample comes from a normal distribution.Use the critical value approach.

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 expected frequency for each group is

Shown below is 2 x 3 contingency table with observed values from a sample of 500.At 95% confidence using the critical value approach,test for independence of the row and column factors.

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.With a .05 level of significance,the critical value for the test is

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: At $\alpha$ = .05 using the p-value approach,test to determine if the votes cast were independent of the sex of the individuals.

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. The results of the survey are shown below. 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.

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

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

From a poll of 800 television viewers,the following data have been accumulated as to their levels of education and their preference of television stations. Test at $\alpha$ = .05 to determine if the selection of a TV station is dependent upon the level of education.Use the p-value approach.

A goodness of fit test is always conducted as a

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.At 95% confidence,the conclusion of the test is that the

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 frequency of seniors is

The results of a recent study regarding smoking and three types of illness are shown in the following table. We are interested in determining whether or not illness is independent of smoking. a.State the null and alternative hypotheses to be tested. b.Show the contingency table of the expected frequencies. c.Compute the test statistic. d.The null hypothesis is to be tested at 95% confidence.Determine the critical value for this test.What do you conclude? e.Determine the p-value and perform the test.

The degrees of freedom for a contingency table with 6 rows and 3 columns is

The sampling distribution for a goodness of fit test is 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 expected frequency of exactly 3 cars arriving in a 10-minute interval is