Exam 13: Chi-Square Applications

Video The owner of a video store is interested in whether or not there is a difference in the proportions of VCR movies rented by members and non-members among movie titles.Three movies are selected and each person who rents them is identified as a member or non-member.A total of 350 people rent these movies and the responses are: Mo vie Membershị Witness Rambo Karate Kid Total Member 21 14 70 105 Non-Member 79 86 80 245 |Total 100 100 150 350 -What is the computed value of the test statistic?

In what way are the chi-square and normal distributions related?

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

Which of the following tests will determine whether sample data could have been drawn from a population having a specified probability distribution?

In preparing a confidence level for a population variance,the size of the sample is 13 and the level of confidence is 0.95.What are the appropriate table values for this interval? ____________________ and ____________________

Grade distribution A professor would like to test to see if the grade distribution for male and female students are the same.The following table shows the distribution of grades for 1450 students. A B Tatal Male 124 192 212 15 Female 195 238 24 120 27 Tatal 319 430 452 207 42 1450 -Using $\alpha$ = 0.05,state the conclusion.

Employee Four employees are monitored to determine whether there is any difference in the proportions of acceptable parts produced by the employees.The sample of parts produced is given below. Employee Quality Total Acceptable 265 270 225 180 950 Unacceptable 10 5 15 20 50 Total 275 275 250 200 1000 These data provide the information for testing the hypothesis that the proportion of unacceptable is the same for the four employees.What is the conclusion?

The realtor for an exclusive,planned housing development says that house prices average $125 thousand and uniformity of prices within the development is indicated by the standard deviation of $ $\sigma ^ { 2 } > 64$ 8 thousand.A prospective buyer wants to check on the uniformity of prices and randomly samples 12 houses and determines the selling price.These data are: 113.0,126.2,134.4,129.4,106.6,117.4,123.5,121.0,109.6,119.4,126.6,and 119.6.Use these data to test the hypothesis: H₀: $\sigma ^ { 2 } \leq 64$ (realtor correct) H₁: (realtor incorrect) The buyer assumes selling prices are normally distributed and employs a 0.05 significance level.Is the statement by the realtor correct? Test statistic = ____________________ Critical Value = ____________________ Conclusion: _____________________ Interpretation: _____________________________________

A chi-square goodness-of-fit test is always conducted as:

A left tail area in the chi-square distribution equals 0.95.For df = 10,the table value equals:

Grade distribution A professor would like to test to see if the grade distribution for male and female students are the same.The following table shows the distribution of grades for 1450 students. A B Tatal Male 124 192 212 15 Female 195 238 24 120 27 Tatal 319 430 452 207 42 1450 -Using $\alpha$ = 0.05,state the decision rule in terms of the critical value.

Which of the following tests do not use the chi-square distribution?

The purpose of the chi-square analysis to test the independence of two variables is to determine the exact nature of the relationship between two ratio variables.

The area to the right of a chi-square value is 0.025.For 5 degrees of freedom,the table value is:

TV Model Three hundred individuals were asked to view the picture quality of four different TVs and asked to choose the one they preferred.The data is shown in the following table: TV Madel Number Wha preferred A 73 D Tatal 300 -Test the equality of proportions at the 0.05 level. What are the null and alternative hypotheses?

Number of sales A salesperson makes five calls per day.A sample of 200 days gives the frequencies of sales volumes listed below Number of Sales Observed Frequency (days) 0 10 1 38 2 69 3 63 4 18 5 2 -Assume the population is a binomial distribution with a probability of purchase $\pi$ equal to 0.50.Compute the expected frequencies (E_j)for the number of sales by using the binomial tables.Combine if necessary to satisfy the rules of five.

A sport preference poll showed the following data for men and women: Favorite Sport Gender Baseball Baskethall Foothall Golf Teruis Male 24 17 30 18 22 Female 21 20 22 12 28 Use the 5% level of significance and test to determine whether sport preferences depend on gender. H₀: _______________________________________________________________ H₁: _______________________________________________________________ Test statistic = ____________________ Critical Value = ____________________ Conclusion: _________________________

The chi-square distribution is used in:

Metro Bus System The management of the Metro Bus System of Houston,TX was faced with the task of improving efficiency in terms of running on time.One of its greatest problems was breakdown of equipment.Between 1994 and 1997,emphasis was placed on maintenance.Random samples of 10,000 bus runs were taken from the records of 1994 and 1997.The percentage of breakdowns in 1994 was 0.4 and in 1997 it was 0.04.Use a chi-square test for equal proportions to analyze these data. -What are the expected frequencies of the 1994 and 1997 breakdowns? 1994: ____________________ 1997: ____________________

Survey In a survey of 100 males and 100 females at a regional university,26 percent of the males and 18 percent of the females responded that they were offended by frequently aired television.The test question is: Could these results indicate that the same proportions of the two samples are offended? -Calculate the expected frequencies of the males and females who are offended by the ads. Males: ____________________ Females: ____________________