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A.

Health insurance benefits vary by the size of the company. The sample data below show the number of companies providing health insurance for small, medium, and large companies. For purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1,000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company. Size of the Company Health Insurance Small Medium Large Yes 33 52 85 No 17 13 15 (a) Perform a test of independence to determine if health insurance coverage is related to the size of the company. State the null and alternative hypotheses. O Ho: Having health insurance is not independent of the size of the company. H: Having health insurance is independent of the size of the company. O Ho: Having health insurance is independent of the size of the company. He: Having health insurance is not independent of the size of the company. O Ho: Having health insurance is not independent of the size of the company. He: The proportion of companies with health insurance benefits is not equal for small, medium and large companies. O Ho: Having health insurance is independent of the size of the company. He: The proportion of companies with health insurance benefits is equal for small, medium and large companies. Compute the expected frequency for the event that a Small Company has health insurance. Assume that the value of the test statistic was computed to be 8.02083 . What is the corresponding p-value? (Round your answer to four decimal places.) p-value =[ Using a 0.05 level of significance, what is your conclusion? O Reject Ho. We conclude health insurance coverage is not independent of the size of the company. O Reject Ho. We conclude health insurance coverage is independent of the size of the company. O Do not reject H. We cannot conclude health insurance coverage is independent of the size of the company. O Do not reject Ho. We cannot conclude health insurance coverage and the size of the company are not independent. (b) A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the above data to support this conclusion. (Round your answers to the nearest integer.) For small companies, |% do not provide health insurance. For medium companies, |% do not provide health insurance. For large companies, % do not provide health insurance. These percentages support the conclusion that small companies are ---Select--- likely to provide health insurance coverage when compared to medium and large companies.A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, & to 6.2 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow. Age Group Hours of Sleep 39 or younger | 40 or older Fewer than & 29 37 6t 6.9 60 57 7t07.9 77 75 g or more 64 91 (a) Conduct a test of independence to determine whether hours of sleep are independent of age (b} What is your estimate of the percentages of individuals who sleep fewer than & hours, 6 to 6.9 hours, 7 to 7.9 hours, and & hours or more per night? A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow. Age Group Hours of Sleep 39 or younger 40 or older Fewer than 6 40 38 6 to 6.9 58 5 7 to 7.9 77 75 8 or more 65 92 (a) Conduct a test of independence to determine whether hours of sleep are independent of age. State the null and alternative hypotheses. O Ho: Hours of sleep per night is independent of age. He : Hours of sleep per night is not independent of age. O Ho: Hours of sleep per night is not independent of age. Ha: Hours of sleep per night is independent of age. O Ho: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups. He : The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups. O Ho: Hours of sleep per night is mutually exclusive from age. H2 : Hours of sleep per night is not mutually exclusive from age. Find the value of the test statistic. (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value =[ Using a 0.05 level of significance, what is your conclusion? Do not reject Ho. We cannot conclude that hours of sleep per night and age are independent. O Do not reject H. We cannot conclude that hours of sleep per night and age are not independent. O Reject Ho. We conclude that hours of sleep per night and age are independent. O Reject Ho. We conclude that hours of sleep per night and age are not independent. (b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night? Round your answers to 1 decimal place. Fewer than 6 % 6 to 6.9 % 7 to 7.9 8 or moreTest the following hypotheses by using the :}_"2 goodness of fit test. HQ: P, = 0.40, og = 0.40, and b= 0.20 H_: The population proportions are not p, = 0.40, p, = 0.40, and p. = 0.20. A sample of size 200 yielded 20 in category A, 160 in category B, and 20 in category C. Use @ = 0.01 and test to see whether the proportions are as stated in Ho' (a) Use the p-value approach. (b) Repeat the test using the critical value approach. Test the following hypotheses by using the ;{2 goodness of fit test. Hg: b, = 0.40, pg = 0.40, and p_ = 0.20 H_: The population proportions are not p, = 0.40, pg = 0.40, and p_ = 0.20. A sample of size 200 yielded 20 in category A, 60 in category B, and 120 in category C. Use o = 0.01 and test to see whether the proportions are as stated in H,,. (a) Use the p-value approach. Find the value of the test statistic. Find the p-value. {Round vour answer to four decimal places.) palve = State your conclusion. L Do not reject H,. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. O Do not reject HD. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. ) Reject Hg. We conclude that the proportions are equal to 0.40, 0.40, and 0.20. L Reject H,. We conclude that the proportions differ from 0.40, 0.40, and 0.20. (b} Repeat the test using the critical value approach. Find the value of the test statistic. L 1 State the critical values for the rejection rule. (If the test is one-tziled, enter NOME for the unused tail. Round your answers to three decimal places.) test statistic = test statistic State your conclusion. L Reject H,. We conclude that the proportions are equal to 0.40, 0.40, and 0.20. I O Do not reject HD. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. 0 Do not reject H,. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. L Reject H,. We conclude that the proportions differ from 0.40, 0.40, and 0.20. During the first 13 weeks of the television season, the Saturday evening 8:00 p.m. to 9:00 p.m. audience proportions were recorded as ABC 31%, CBS 26%, NBC 27%, and independents 16%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 97 homes, CBS 68 homes, NBC 91 homes, and independents 44 homes. Test with a = 0.05 to determine whether the viewing audience proportions changed. State the null and alternative hypotheses. O Ho: PABC = 0.31, Pces = 0.26, PNBC = 0.27, PIND = 0.16 H2: The proportions are not PABC = 0.31, Pces = 0.26, PNBC = 0.27, PIND = 0.16. O H.: The proportions are not PABC = 0.31, PCBS = 0.26, PNBC = 0.27, PIND = 0.16. Ha: PABC = 0.31, PCBS = 0.26, PNBC = 0.27, PIND = 0.16 O Ho: PABC = 0.31, Pces = 0.26, PNBC = 0.27, PIND = 0.16 HE: PABC # 0.31, PCBS # 0.26, PNBC # 0.27, PIND # 0.16 O Ho: PABC # 0.31, Pces # 0.26, PNBC # 0.27, PIND = 0.16 Hai PABC = 0.31, PCBS = 0.26, PNBC = 0.27, PIND = 0.16 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Do not reject H. There has been a significant change in the viewing audience proportions. O Reject Ho. There has been a significant change in the viewing audience proportions. O Reject Ho. There has not been a significant change in the viewing audience proportions. O Do not reject H . There has not been a significant change in the viewing audience proportions.The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week. Assume that a sample of 420 accidents provided the following data Sunday Monday Tuesday Wednesday Thursday Friday Saturday 66 50 53 47 55 69 80 (a) Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. Use a 0.05 level of significance. State the null and alternative hypotheses. O H: Not all proportions are equal. Hai Psun = PMon = PTue = PWed = PThu = PFri = Psat = O Ho: Psun # PMon * PTue # PWed * PThu * PFri * Psat He: All proportions are equal. O Ho: Not all proportions are equal. Hai Psun * PMon # PTue * Pwed * PThu * PFri * Psat # = O Hoi Psun = PMon = PTue = PWed = PThu = PFri = PSat H: Not all proportions are equal. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Do not reject H . We conclude that the proportion of traffic accidents is the same for each day of the week. O Reject Ho. We conclude that the proportion of traffic accidents is the same for each day of the week. O Reject Ho. We conclude that the proportion of traffic accidents is not the same for each day of the week. O Do not reject Ho. We conclude that the proportion of traffic accidents is not the same for each day of the week. (b) Compute the percentage of traffic accidents occurring on each day of the week. (Round your answers to two decimal places.) Sunday % Monday Tuesday % Wednesday Thursday % Friday Saturday % What day has the highest percentage of traffic accidents?Based on sales over a six-month period, the five top-selling compact cars are Chevy Cruze, Ford Focus, Hyundai Elantra, Honda Civic, and Toyota Corolla. Based on total sales, the market shares for these five compact cars were Chevy Cruze 24%, Ford Focus 21%, Hyundai Elantra 20%, Honda Civic 18%, and Toyeta Corolla 17%. Suppose a sample of 400 compact car sales in one city showed the following number of vehicles sold. Chevy Cruze 108 Ford Focus 93 Hyundai Elantra | 64 Honda Civic 84 Toyota Corolla | 51 Use a goodness of fit test to determine if the sample data indicate that the market shares for the five compact cars in this city are different than the market shares reported by Motor Trend. Use 2 0.05 level of significance State the null and alternative hypotheses. H,: The majority of the market shares for the five automobiles in this ity differ from the ones reported by Motor Trend. H,: The majority of the market shares for the five automobiles in this city are the same as the ones reported by Motor Trend. Hg: The market shares for the five autemobiles in this city differ from 0.24, 0.21, 0.20, 0.18, 0.17. H_: The market shares for the five automobiles in this city are the same as the above shares. H i The market shares for the five automobiles in this dty are 0.24, 0.21, 0.20, 0.18, 0.17. H,: The market shares for the five automobiles in this city differ from the above shares. Hyi The majority of the market shares for the five autemobiles in this city are the same as the ones reported by Moter Trend. H_: The majority of the market shares for the five automobiles in this city differ from the ones reported by Motor Trend. Find the value of the test statistic. (Round your answer to three decimal places.) Find the critical value for the test. (Round your answer to three decimal places.) critical value = State your condlusion > Do not reject 4. We conclude that the market shares for the five compact cars in this city differ from the market shares reported. Reject H;. We cenclude that the market shares for the five compact cars in this city differ from the market shares reported. Reject H,. We cannot conclude that the market shares for the five compact cars s city differ from the market shares reported. Do not reject H,. We cannot condlude that the market shares for the five compact cars in this city differ from the market shares reported. What market share differences, if any, exist in this city? Chevy Cruze shows [Seleciv | market share in this city. Ford Focus shows [Seleci v | market share in this city. Hyundai Elantra shows Seleci v | market share in this city. Honda Civic shows [Select- v | market share in this city. Toyota Cerolla shows [Sslect v market share in this city. Based on 2017 sales, the six top-selling compact cars are the Honda Civic, Toyota Coralla, Nissan Sentra, Hyundai Elantra, Chevrolet Cruze, and Ford Focus,t The 2017 market shares are: Honda Civic 20%, Toyota Corolla 17%, Nissan Sentra 12%, Hyundai Elantra 10%, Chevrolet Cruze 10%, and Ford Focus 8%, with other small car models making up the remaining 239%. Suppose a sample of 400 compact car sales in a certain large city showed the following number of vehicles sold. Honda Civic o9 Toyota Corolla | 71 Nissan Sentra 55 Hyundai Elantra | 45 Chevrolet Cruze | 41 Ford Focus 26 Others 62 Use a goodness of fit test to determine if the sample data indicate that the market shares for compact cars in the ity are different than the market shares suggested by nationwide 2017 sales. Use a 0.05 level of significance. State the null and alternative hypothesis. H,: The market shares for the compact cars in the city are different from at least one of the nationwide market shares listed. H_: The market shares for the compact cars in the city are not different from any of the nationwide market shares listed. Hy: The market shares for the compact cars in the city do not differ from market shares nationwide. H_: The market shares for the compact cars in the city differ from market shares nationwide. ) H,: The market shares for the compact cars in the city differ from market shares nationwide. he market shares for the compact cars in the city do not differ from market shares nationwide. H,: The market shares for the compact cars in the city are not different from any of the nationwide market shares listed. H_: The market shares for the compact cars in the city are different for at least one of the nationwide market shares listed Find the value of the test statistic.(Round your answer te two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion Reject H,. We cannot conclude that market shares for the compact cars in the city differ from the nationwide market shares. Reject H,. We conclude that market shares for the compact cars in the city differ from the natienwide market shares. Do not reject 4. We cannot conclude that market shares for the compact cars in the city differ from the nationwide market shares. ) Do not reject H. We conclude that market shares for the compact cars in the city differ from the nationwide market shares