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- The Office of the University Registrar of Seoul University would like to know if the degree programs in College of Science and Math are equally preferred by students. Furthermore, the office would like to know if such degree programs are related to the gender of the students. The test claim that the proportions of the students enrolled are equal in each degree program at alpha=0.05 Using the data on the number of currently enrolled students in each gender (M of F) in each of the four degree programs, find the: a. Table showing the observed and expected values b. Chi-square critical Value c. Chi-square test statistic d. Accept or Reject the null hypothesis?If X1, X2, ... , Xn constitute a random sample from anormal population with μ = 0, show that ni=1X2inis an unbiased estimator of σ2.Let $X$ and $Y$ be random variables with the space consisting of the four points (0,0),(1,1),(1,0),(1,-1) . Assign positive probabilities to these four points so that the correlation coefficient is equal to zero. Are $X$ and $Y$ independent?
- An urn contains 10 white balls and 8 red balls. 2 balls are selected at random. Let X denote the number of red balls drawn and let Y denote the number of white balls drawn. Find the correlation coefficient between X and Y.Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)?Laureysens studied the concentration of aluminum in wood from anumber of clones of poplar growing in an area with heavy pollution. The same clone wassampled and tested once in August and again in November. The researchers believed that theconcentration of aluminum would be shown to be increasing over time—and hence would behigher in November than in August. The following table gives the aluminum concentrationsfor 12 of the clones.Use the Wilcoxon signed rank test to see if there is a difference in the concentration ofaluminum. Perform the test on the 5% level. What is your conclusion?
- If the alleles A and B of the cystic fibrosis gene occur in a population with frequencies p and 1 - p (where pis between 0 and 1), then the frequency of heterozygous carriers (carriers with both alleles) is 2p(l - p). Which value of p gives the largest frequency of heterozygous carriers?Suppose that X1, ..., Xn are random variables such that the variance of each variable is 1 and the correlation between each pair of different variables is 1/4. Determine Var (X1 + ...+Xn).Suppose a sample of 950 men found that 642 of them favored the death penalty for capital murder convictions while a sample of 810 women found that 405 of them favored the death penalty for capital murder convictions. Test the claim using a signifiance level of 0.05 that the proportion of men favoring the death penalty is greater tha nthe proportion of women favoring the death penalty. Let p1 = proportion of men favoring the death penalty Let p2 = proportion of women favoring the death penalty Answer the following questions below based upon the above data and the definitions of p1 and p2 Which group of statements correctly describe the Claim, the Null Hypothesis, and the Alternative Hypothesis:
- Suppose a sample of 950 men found that 642 of them favored the death penalty for capital murder convictions while a sample of 810 women found that 405 of them favored the death penalty for capital murder convictions. Test the claim using a signifiance level of 0.05 that the proportion of men favoring the death penalty is greater tha nthe proportion of women favoring the death penalty. Let p1 = proportion of men favoring the death penalty Let p2 = proportion of women favoring the death penalty Answer the following questions below based upon the above data and the definitions of p1 and p2 a) What is the type of Test? b) What is/are the critical values(s) c) What is the value of the test statistic? d) What is the decision? e) What is the conclusion?Suppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2)μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2 ? 3(2.7)−7(4.2)=−21.33(2.7)−7(4.2)=−21.3 A 3−7=−43−7=−4 B 2.7−4.2=−1.52.7−4.2=−1.5 C…