Exam 11: Chi-Square and Analysis of Variance

The following table represents the number of absences on various days of the week at an_ elementary school. Monday Tuesday Wednesday Thursday Friday 45 32 17 25 38 Identify the critical value for a goodness-of-fit test, assuming a 0.05 significance level.

Use a $X^2$ test to test the claim that in the given contingency table, the row variable and the column variable are independent. The table below shows the age and favorite type of music of 668 randomly selected people. Rock Pop Classical 50 85 73 68 91 60 35-45 90 74 77 Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.

Goodness-of-fit hypothesis tests are always___________________._

A survey of students at a college was asked if they lived at home with their parents, rented an apartment, or owned their own home. The results are shown in the table below sorted by gender. $\text { At } \alpha = 0.10$ test the claim that living accommodations are independent of the gender of the student. Live with Parent Rent Apartment Own Home Male 20 26 19 Female 22 28 26

In conducting a goodness-of-fit test, a requirement is that __________________________._

Perform the indicated goodness-of-fit test. Among the four northwestern states, Washington has_ 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 1000 subjects has a distribution that agrees with the distribution of state populations.

Perform the indicated goodness-of-fit test. A company manager wishes to test a union leader's_ claim that absences occur on the different week days with the same frequencies. Test this claim at the 0.05 level of significance if the following sample data have been compiled. Day Mon Tue Wed Thurs Fri Absences 37 15 12 23 43

Responses to a survey question about color preference for a candy are broken down according to gender in the table given below. At the 0.05 significance level, test the claim that candy Color preference and gender are independent. Red Blue Yellow Male 25 50 15 Female 20 30 10 What is your conclusion about the null hypothesis and about the claim?

The following are the hypotheses for a test of the claim that college graduation statue and cola preference are independent. H₀: College graduation status and cola preference are independent. H₁: College graduation status and cola preference are dependent. If the test statistic: χ2 = 0.579 and the critical value is χ2 = 5.991, what is your conclusion About the null hypothesis and about the claim?

In studying the occurrence of genetic characteristics, the following sample data were_ obtained. You would like to test the claim that the characteristics occur with the same Frequency at the 0.05 significance level. Characteristic A B C D E F Frequency 28 30 45 48 39 39 What is the expected value for D?

In studying the occurrence of genetic characteristics, the following sample data were_ obtained. You would like to test the claim that the characteristics occur with the same Frequency at the 0.05 significance level. What is value of the test statistic? Characteristic A B C D E F Frequency 28 30 45 48 39 39

The following table represents the number of absences on various days of the week at an_ elementary school. Monday Tuesday Wednesday Thursday Friday 45 32 17 25 38 Identify the number of degrees of freedom for a goodness-of-fit test (for a uniform Distribution), assuming a 0.05 significance level.

Describe the null hypothesis for the test of independence. List the assumptions for the $X^2$ test_ of independence.

A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below. College A College B College C College D Smoke 17 26 11 34 Don't Smoke 83 74 89 66 Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges.

Explain the computation of expected values for contingency tables in terms of probabilities._ Refer to the assumptions of the null hypothesis as part of your explanation. You might give a brief example to illustrate.

For a recent year, the following are the numbers of homicides that occurred each month in New_ York City: 38, 30, 46, 40, 46, 49, 47, 50, 50, 42, 37, 37. Use a 0.05 significance level to test the claim that homicides in New York City are equally likely for each of the 12 months. State your Conclusion about the claim.

In studying the responses to a multiple-choice test question, the following sample data were_ obtained. At the 0.05 significance level, test the claim that the responses occur with the same frequency. Response A B C D E Frequency 12 15 16 18 19

At a high school debate tournament, half of the teams were asked to wear suits and ties_ and the rest were asked to wear jeans and t-shirts. The results are given in the table below. In Order to test the claim at the 0.05 level that the proportion of wins is the same for teams Wearing suits as for teams wearing jeans, what would the null hypothesis be? Win Loss Suit 22 28 T-Shirt 28 22 A)The proportions of wins is the same for teams wearing suits as for teams wearing jeans. B)The proportions of wins is different for teams wearing suits as for teams wearing jeans. C)The mean number of wins is the same for teams wearing suits as for teams wearing jeans. D)The mean number of wins is the same for teams wearing suits as for teams wearing jeans.

According to Benford's Law, a variety of different data sets include numbers with leading (first)1)____________ digits that follow the distribution shown in the table below. Test for goodness-of-fit with Benford's Law. Leading Digit 1 2 3 4 5 6 7 8 9 Benford's law: distribution of leading digits 30.1\% 17.6\% 12.5\% 9.7\% 7.9\% 6.7\% 5.8\% 5.1\% 4.6\% When working for the Brooklyn District Attorney, investigator Robert Burton analyzed the Leading digits of the amounts from 784 checks issued by seven suspect companies. The Frequencies were found to be 0, 12, 0, 73, 482, 186, 8, 23, and 0, and those digits correspond to the Leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequenciesare Substantially different from the frequencies expected with Benford's Law, the check Amounts appear to result from fraud. Use a 0.05 significance level to test for Goodness-of-fit with Benford's Law. What is the value of the test statistic? Does it appear that the Checks are the result of fraud?

Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?_