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1. Determine the appropriate test to be used in the following exercise.An archaeologist is calculating the distribution of the frequency of the number of artifacts she finds in a dig site. Based on previous digs, the archaeologist creates an expected distribution broken down by grid sections in the dig site. Once the site has been fully excavated, she compares the actual number of artifacts found in each grid section to see if her expectation was accurate.test for homogeneitygoodness-of-fit test test of a single variancetest of independencecomparison of Chi-square tests2. Determine the appropriate test to be used in the following exercise.The owner of a baseball team is interested in the relationship between player salaries and team winning percentage. He takes a random sample of 100 players from different organizations.goodness-of-fit testcomparison of Chi-square tests test for homogeneitytest of independencetest of a single variance3. The marital status distribution of the U.S. male population, age 15 and older, is as shown below.Marital StatusPercentnever married31.3married56.1widowed2.5divorced/separated10.1Suppose that a random sample of 400 U.S. young adult males, 18 to 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population at the 5% level. Calculate the frequency one would expect when surveying 400 people. Fill in the table below, rounding to two decimal places.Marital StatusFrequencyExpected Frequencynever married139married237widowed3divorced/separated21What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)What is the test statistic? (Round your answer to two decimal places.)What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =5. A particular city has an Asian population of 1419 people, out of a total population of 23,609. Conduct a goodness of fit test at the 5% level to determine if the self-reported sub-groups of Asians are evenly distributed. Round expected frequency to two decimal places.RaceFrequencyExpected FrequencyAsian Indian136Chinese115Filipino1041Japanese82Korean13Vietnamese9Other23What are the degrees of freedom?What is the test statistic? (Round your answer to two decimal places.)What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write the appropriate conclusion.(i) Alpha:α =6.The table below contains information from a survey among 499 participants classified according to their age groups. The second column shows the percentage of obese people per age class among the study participants. The last column comes from a different study at the national level that shows the corresponding percentages of obese people in the same age classes in the USA. Perform a hypothesis test at the 5% significance level to determine whether the survey participants are a representative sample of the USA obese population.Age Class (Years)Obese (Percentage)Expected USA average (Percentage)20–3075.032.631–4027.532.641–5014.636.651–6022.936.661–7021.039.7What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.) What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.) α =7. A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Test to see if the best ski area is independent of the level of the skier. (Use a significance level of 0.05.)U.S. Ski AreaBeginnerIntermediateAdvancedTahoe193042Utah113161Colorado84150What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)What is the test statistic? (Round your answer to two decimal places.)What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write the appropriate conclusion.(i) Alpha:α =8. Car manufacturers are interested in whether there is a relationship between the size of car an individual drives and the number of people in the driver’s family (that is, whether car size and family size are independent). To test this, suppose that 803 car owners were randomly surveyed with the following results. Conduct a test for independence at the 5% level.Family SizeSub & CompactMid-sizeFull-sizeVan & Truck1203641342215170793 – 4205099895+20317171What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)What is the test statistic? (Round your answer to two decimal places.)What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =9. College students may be interested in whether or not their majors have any effect on starting salaries after graduation. Suppose that 298 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Below are the data. Conduct a test of independence. (Use a significance level of 0.05.)Major< $50,000$50,000 – $68,999$69,000 +English4204Engineering103060Nursing101514Business102029Psychology213021What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)What is the test statistic? (Round your answer to two decimal places.)What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)α = 10. A manager of a sports club keeps information concerning the main sport in which members participate and their ages. To test whether there is a relationship between the age of a member and his or her choice of sport, 635 members of the sports club are randomly selected. Conduct a test of independence at the 5% level.Sport18 – 2526 – 3031 – 4041 and overracquetball40602844tennis59753663swimming70596734What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)What is the test statistic? (Round your answer to two decimal places.)What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =11. Suppose that 610 30-year-olds were surveyed to determine whether or not there is a relationship between the level of education an individual has and salary. Conduct a test of independence at the 5% level.Annual SalaryNot a high schoolgraduateHigh schoolgraduateCollegegraduateMasters ordoctorate< $30,0001520155$30,000 – $40,00025457030$40,000 – $50,00010204055$50,000 – $60,0005151560$60,000+0510150What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)What is the test statistic? (Round your answer to two decimal places.)What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =12. A psychologist is interested in testing whether there is a difference in the distribution of personality types for business majors and social science majors. The results of the study are shown in the table below. Conduct a test of homogeneity. Test at a 5% level of significance.OpenConscientiousExtrovertAgreeableNeuroticBusiness4352476359Social Science7275648267What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)What is the test statistic? (Round your answer to two decimal places.)What is the p-value? (Round your answer to four decimal places.)Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =13. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in the table below. Conduct a test for homogeneity at a 5% level of significance.French ToastPancakesWafflesOmelettesMen43352853Women65595560What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.) Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.) α =