​​​ 1. What conditions are necessary to use the chi-square goodness-of-fit test? 2. Find the expected frequency, Ei, for the given values of n and pi. n = 140, pi = 0.6 3. A survey was conducted two years ago asking college students their top motivations for using a credit card. To determine whether this distribution has changed, you randomly select 425 college students and ask each one what the top motivation is for using a credit card. Can you conclude that there has been a change in the claimed or expected distribution? Use α = 0.10. Complete parts (s) through (d). a. State H0 and Ha and identify the claim. b. Determine the critical value, χ20, and the rejection region. c. Calculate the test statistic. d. Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. 4. The national distribution of fatal work injuries in a country is shown in the table to the right under National %. You believe that the distribution of fatal work injuries is different in the western part of the country and randomly select 6231 fatal work injuries occurring in that region. At α = 0.10 can you conclude that the distribution of fatal work injuries in the west is different from the national distribution? Complete parts a through d below. a. State H0 and Ha and identify the claim. b. Determine the critical value, χ20, and the rejection region. c. Calculate the test statistic. d. Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. 5. The frequency distribution shows the results of 200 test scores. Are the test scores normally distributed? Use α = 0.05. Complete parts (a) through (d). Class boundaries 49.5-58.5 58.5-67.5 67.5-76.5 76.5-85.5 85.5-94.5 Frequency, f 19 60 84 33 4 Using a chi-square goodness-of-fit test, you can decide with some degree of certainty, whether a variable is normally distributed. In all chi-square test for normally, the null and alternative hypotheses are as follows. H0: The test scores have a normal distribution. Ha: The test scores do not have a normal distribution. a. Find the expected frequencies. b. Determine the critical value, χ20, and the rejection region. c. Calculate the test statistic. d. Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. 6. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. If the test statistic for the chi-square independence test is large, you will, in most cases, reject the null hypothesis. 7. Use the contingency table to the right to calculate the marginal frequencies and find the expected frequency for each cell in the contingency table. Assume that the variables are independent. Athlete has Result Stretched Not stretched Injury 17 20 No injury 203 183 8. You want to determine whether the reason given by workers for continuing their education is related to job type. In the study, you randomly collect the data shown in the contingency table. At α = 0.01, can you conclude that the reason and type of worker are dependent? Complete parts (a) through (d). Reason Type of worker Professional personal Both Technical 38 36 35 Other 46 26 34 a. Identify the claim and state the null and alternative hypotheses. b. Determine the degree of freedom, find the critical value, and identify the rejection region. c. Calculate the test statistic. If convenient, use the technology. d. Decide to reject or fail to reject the null hypothesis. Can you conclude that the reason and type of worker are dependent? 9. The contingency table below shows the results of a sample of motor vehicle crash deaths by age and gender. At α = 0.025, perform a homogeneity of proportions test on the claim that the proportions of motor vehicle crash death involving males or females are the same for each group. Age Gender 16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 and older Male 96 73 68 69 32 29 25 7 Female 41 20 27 31 22 20 18 10 10. The contingency table below shows the number of adults in a nation (in million) ages 25 and over by employment status and educational attainment. Rewrite the frequencies in the table as relative frequencies by dividing each frequency by the sample size. Educational Attainment Status Not a high school graduate High school graduate Some college, no degree Associate's, bachelor's, or advanced degree Employed 8.5 31.9 25.6 41.7 Unemployed 2.5 2.2 1.3 3.6 Not in the labor force 11.9 24.3 5.6 14.3 11. The contingency table below shows the number of adults in a nation (in million) ages 25 and over by employment status and educational attainment. The frequencies in the table can be written as relative frequencies by dividing each frequency by the sample size. Educational Attainment Status Not a high school graduate High school graduate Some college, no degree Associate's, bachelor's, or advanced degree Employed 12.5 28.7 27.6 44.4 Unemployed