Graduate ProgramsMany graduate programs require students to pass a comprehensiveexam (or qualifying exam, or something equivalent) before beingadmitted into candidacy to receive the degree.Of interest is to determine the mean age of students at the timethey take the comprehensive exam for all students enrolled ingraduate programs that require students to takecomprehensive exams.23Based on the information provided, what is the population ofinterest?all students enrolled in graduate programsall students at the universitymean age of all students enrolled in graduate programs that requirestudents take comprehensive exams.Oall students enrolled in graduate programs that require students to takecomprehensive exams.--Consider the statement in question 2. Based on this, using both theappropriate symbol and in words, what is the parameter of interest?μ = the mean age of studentsDOμ = the mean age of students at the time they take the comprehensiveexam for all students enrolled in graduate programs that require studentsto take comprehensive exams.TT=the mean age of students at the time they take the comprehensiveexam for all students enrolled in graduate programs that requirestudents to take comprehensive exams.all students enrolled in graduate programs that require students totake comprehensive exams. Preparing for Comprehensive ExamsStudents preparing for comprehensive exams usually spendmany hours studying. Suppose it is known that the timestudents spend studying for comprehensive exams has adistribution that is skewed heavily to the right with a mean of41.3 hours and a standard deviation of 6.8 hours. If a simplerandom sample of 72 students is selected and the amount oftime each spent studying for the comprehensive exam isdetermined.45State and check the two assumptions.Population is skewed heavily to the right and therefore the Central Limittheorem does not apply.The sample size is large enough to apply the Central Limit Theorem (n =72 > 40).We have a simple random sample, and the sample size is large enough toapply the Central Limit Theorem (n = 72 > 40).We do not have a simple random sample.Describe completely the sampling distribution of X, the resulting mean amountof time spent studying for this sample of 72 students.X-N (41.3, 0.307).X-N (6.8, 4.867).X-N (41.3, 0.801).X-N (41.3, 0.094)Submit

From the information, the interest is to determine the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams.Question 2)The population of interest would be the mean age of all students enrolled in graduate programs that require students to take comprehensive exams.Thus, the correct option would be third option. Question 3) The parameter of interest is denoted by population mean μ.In terms of symbols, the parameter of interest is, μ = the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams.The correct option would be second option.Students preparing for comprehensive exams usually spend many hours studying. Suppose it is known that the time students spend studying for comprehensive exams has a distribution that is skewed heavily to the right with a mean of 41.3 hours and a standard deviation of 6.8 hours. If a simple random sample of 72 students is selected and the amount of time each spent studying for the comprehensive exam is determined. Question 4)The assumptions to apply central limit theorem is, 1. The sample drawn is simple random sample and 2. If the distribution has skew, then the larger sample size needed is greater than or equal to 40.From the given information, the sample drawn is simple random sample and the sample of 72 students ( >40)Therefore, the correct option would be third option.i.e., We have a simple random sample, and the sample size is large enough to apply the Central Limit Theorem (n = 72 > 40). From the given information, mean has 41.3 hours and a standard deviation has 6.8 hours.i.e., μ=41.3 and σ=6.8.The sample size is, n=72The sampling distribution of x¯ follows normal distribution with mean μx¯=μ =41.3and standard deviation σx¯=σn =6.872 =0.801Thus, x¯ ~N(41.3,0.801).option(3) is the correct choice.