5 Questions- Business StatisticsHI,I need detailed solutions for all the questions in the attached file. I need a score of atleast 85% in the testThanks
1STAT2112.10 NAME:__________________GWID:G__________Fall 2020 sba Midterm-Part II (Open Book)Due: 5pm, October 31, 2020 SHOW ALL YOUR WORKAnswer all the questions using very DARK Black Ink Pen and showALL your work when needed. Good Luck. Email me your answers inthe format as instructed.Problem 1. These days you hear a lot about vaccines for Covid-19 that are in Phase IIIrandomized clinical trials. I was unable to find a real data on Covid-19 vaccines. However,below is the data on a high-dose, trivalent, inactivated influenza vaccine (IIV3-HD) as comparedto a standard-dose flu vaccine. The high-dose is marketed as a better influenza vaccine foradults 65 years of age or older. This study evaluated whether IIV3-HD also improves protectionagainst laboratory-confirmed influenza illness. Thirty-two (32) adults 65 years of age or olderwere randomized into two groups pf High and Standard Dose flu vaccines and frequencies ofresponse at 3-levels were measured.Level of responseNone Partial CompleteStandard 8 2 6High-Dose 1 3 12a. State your null and alternative hypotheses (2 pts)b. Test your above hypothesis and state and support your conclusion using the MOSTappropriate statistical tool you have learned in this course (15 pts). Use α=0.05.c. If the null is rejected, where the difference is mostly coming from (3 pts).2Question 2. A researcher was interested in investigating a relationship between the age(independent variable) of a driver and the distance the driver can see. For this purpose, hecollected data on 30 drives. The data with some purposefully missing/omitted information isprovided in Appendix “1”. To help you with your analysis, partial summary statistics areprovided below:SSxx = 13,752SSxy = – 41,350SSyy =193,667∑ x = ∑ Age = 1,530; ∑ y = ∑(Distance the driver can see)=12,700a) Write the estimated regression line (4pts)b) Is the relationship meaningful (significant at α=0.05)? (3 pts) – make sure to statethe null and alternative hypothesis first.c) What is the strength of the relationship? It is significant? (2 pts)d) What is the coefficient of determination? (2 pts)e) What is the Adjusted R-sq? (2 pts)f) John is 61 years old. What is the expected driving distance for him? What is the95% prediction interval for John? (2 pts)3Problem 3. Hours of TV watched per week for a random sample of men andwomen from each of three age groups are collected and reported in thefollowing table.Age Group .18-24 25-54 55+20 23 3327 21 33Male 20 23 3922 28 3328 28 3725 32 4419 26 43Female 27 33 5232 33 4331 24 54A) What is the most suitable statistical design to analyze this data (1pt)B) Identify all the factor(s) and level(s) of each factors (2 pts)I analyzed the data for you and the following results .SSTOT=2412.70; SS(gender)= 353.63; SS(Age)=1,520; SSE=429.70.C. Complete the ANOVA Table and test all the null hypotheses you identified aboveand state your conclusions. (7 pts)4Question 4. We are interested in comparing the three varieties of green peas. Forthis, we planted the seeds of these peas in pots arranged randomly and placedrandomly on three floors of a large house in McLean, Virginia. We waited untilthe full growth was achieved. The number incomplete pods in each pot wererecorded and provided in the following table:Floor VarietyA B C1 2 8 102 4 7 93 3 9 11To help you with your analysis, I computed SSTOT=84. Using the mostappropriate analysis method you have learned in this course, analyze the dataat α=0.05. Make sure to state your null hypothesis and carry out the fullanalysis without a use of computer software. Which variety do you recommendand why. (15 pts)5Questions 5. A scientific foundation wanted to evaluate the relation between y=salary of researcher (in thousands of dollars), x1= number of years ofexperience, x2= an index of publication quality, x3=sex (M=1, F=0) and x4= anindex of success in obtaining grant support. A sample of 35 researchers wasrandomly selected. We did a proper analysis and parts of the computerprintout appear below. (1 pt for each question)Predictor Coef SE Coef T P .Constant 17.85 2.00 _ 0.0001 Years 1.10 0.36 0.0032Papers 0.32 0.037 0.0002Sex 1.59 0.69 0.0083Grants 1.29 0.30 0.0003s = 1.75276 R-sq = 92.3% adj R-sq = __.5.1 The least squares line fitted to the data is:a) salary = 2.001 + 0.33 x1 + 0.04 x2 + 0.69 x3 + 0.30 x4 + εb) salary = 17.85 + 1.10 x1 + 0.32 x2 + 1.59 x3 + 1.29 x4 + εc) salary = 2.001 + 0.33 x1 + 0.04 x2 + 0.69 x3 + 0.30 x4d) salary = 17.85 + 1.10 x1 + 0.32 x2 + 1.59 x3 + 1.29 x45.2 The p-value of the ANOVA F test will be:a) very large, because all of the variable are good predictors of salaryb) very small, because all of the variables are good predictors of salaryc) very large, because none of the variables are good predictors of salaryd) very small, because none of the variables are good predictors of salary5.3. The p-value for testing whether salary increases with years of exp. is:a) .0001 b) .0032 c) .0064 d) .00165.4. The independent variable that helps the most in predicting salary is:a) intercept b) years c) papers d) sex e) grants5.5 Which of the following gives a 95% CI for β1?a) 17.847± t* (2.002) b) 17.847± t* (8.915)c) 1.1031± t* (.3596) d) 1.1031 ± t* (3.068)5.6. How many degrees of freedom does the t* values have?a) 34 b) 33 c) 30 d) 4 505.7. Compute the t-values not provided in the table.5.8. Compute the Adjusted R-sq.5.9. Compute the F-Statistics (for the AVOVA Table – for this data).5.10. What is the critical value for the correct F-distribution at α=0.01.6Appendix “1”Age Distance18 51020 59022 56023 510— 46025 49027 —28 51029 46032 410— 42041 46046 45049 38053 46055 42063 35065 42066 30067 41068 30070 39071 32072 37073 28074 42075 46077 36079 31082 360
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