An author argued that more basketball players have birthdates in the months immediately following July 31, because that was the age cutoff date for nonschool basketball leagues. Here is a sample of frequency counts of months of birthdates of randomly selected professional basketball players starting with January: 323, 321, 318, 377, 333, 341, 342, 493, 483, 450, 383, 362 CI . Using a 0.05 signicance level, is there sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency? Do the sample values appear to support the author's claim? Determine the null and alternative hypotheses. H0: Births occur with the same frequency in the different months of the year. H1: At least one month has a different frequency of births than the other months. Calculate the test statistic, X2- x2 = 117.380V (Round to three decimal places as needed.) Calculate the P-value. P-value = (Round to three decimal places as needed.) A classic story involves four carpooling students who missed a test and gave as an excuse a at tire. On the makeup test, the instructor asked the students to identify the particular tire that went at. If they really didn't have a at tire, would they be able to identify the same tire? A statistician asked 50 other randomly selected students to identify the tire they would select. The results are listed in the accompanying table. Use a 0.05 signicance level to test the statistician's claim that the results t a uniform distribution. What does the result suggest about the likelihood of four students identifying the same tire when they really didn't have a at? Tire Left Front Right Front Left Rear Right Rear El Number Selected 13 10 14 13 Determine the null and alternative hypotheses. H0: The tires are selected with the same frequency. H1: At least one tire has a different frequency than the other tires. Calculate the test statistic, x2. X2 = 0.720 (Round to three decimal places as needed.) Calculate the Pvalue. P-value = 0.868 (Round to three decimal places as needed.) What is the conclusion for this hypothesis test? Because the P-value is greater than the signicance level, fail to reject H0. There is not sufcient evidence to warrant rejection of the claim that the results t a uniform distribution. What does the result suggest about the likelihood of four students identifying the same tire when they really didn't have a at'? . Because one of the tires is more likely to be selected than the others, it is likely that each of the four students will select the same tire. Because the results t a uniform distribution, it is likely that each of the four students will select the same tire. . Because the results t a uniform distribution, it is unlikely that each of the four students will select the same tire. . Because one of the tires is less likely to be selected than the others, it is unlikely that each of the four students will select the same tire. Randomly selected deaths of motorcycle riders in a region of the northern hemisphere are summarized in the accompanying table. Use a 0.05 signicance level to test the claim that such fatalities occur with equal frequency in the different months. How might the results be explained? Month Jan. Feb. March April May June :I Number 9 1 1 13 1 6 20 25 Month July Aug. Sept. Oct. Nov. Dec. Number 30 27 28 12 8 9 E) Determine the null and alternative hypotheses. H0: Fatalities occur with the same frequency in the different months of the year. H1: At least one month has a different frequency of fatalities than the other months. Calculate the test statistic, X2- x2 = 43.192 (Round to three decimal places as needed.) Calculate the P-value. Pvalue = 0.000 (Round to three decimal places as needed.) What is the conclusion for this hypothesis test? Because the P-value is less than or equal to the signicance level, reject H0. There is sufcient evidence to warrant rejection of the claim that motorcycle fatalities occur with equal frequency in the different months. How might the results be explained? People are less likely to drive motorcycles during the summer, and more likely during the winter. People are more likely to drive motorcycles during the summer, and less likely during the winter. People are equally likely to drive motorcycles at any time of the year. People are more likely to drive motorcycles during the spring, and less likely during fall. Randomly selected deaths from car crashes were obtained, and the results are obtained in the accompanying table. Use a 0.05 signicance level to test the claim that car crash fatalities occur with equal frequency on the different days of the week. How might the results be explained? Why does there appear to be an exceptionally large number of car crash fatalities on Saturday? Day Sun. Mon. Tues. Wed. Thurs. Fri. Sat. :| Number of Fatalities 130 91 96 95 109 143 152 Determine the null and alternative hypotheses. H0: Fatalities occur with the same frequency on the different days of the week. H1 : At least one day has a different frequency of fatalities than the other days. Calculate the test statistic, x2. x2 = 32.029 (Round to three decimal places as needed.) Calculate the P-value. P-value = (Round to three decimal places as needed.)