6) Suppose the m.g.f. of the r.v. X is given below: MC) : (44/120o) +(4s /no) exp (t) +(20120/1e0mprd) a) Find the mean and variance of X 4((이 120) b) Find P(X>1)
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- The demand for a commodity is given by Q = Bo + B₁P+u, where Q denotes quantity, P denotes price, and u denotes factors other than price that determine demand. Supply for the commodity is given by Q You, where v denotes factors other than price that determine supply. Suppose that u and v both have a mean of zero, have variances o and o2, and are mutually uncorrelated. Solve the two simultaneous equations to show how Q and P depend on u and v.Every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). This year's results were: Aptitude Score 0 1 2 3 4 5 Frequency 4 1 1 4 4 1 The mean (T) aptitude score: The median aptitude score: (Please show your answer to 1 decimal place.) (Please separate your answers by ',' in bimodal situation. Enter DNE The mode aptitude score: if there is no mode.) Textbook Measures of CenterBelow is data of lobster sales volume from a seafood company. We're are using exponential smoothing (α = 0.5) and 3-year moving average to forecast it. a) Fill the blanks above and write your processes below. b) What are the mean absolute deviations (MADs) of the two methods? Whichmethod will you choose based on the results? *Please solve for a-b, either type your work and answers or write them neatly on paper* thank you!
- If the life expectacy in county A is 65 years with CI of (55, 75) and in county B is 87 years with CI of (85, 90), are the two life expectancies likely to be statistically different?Which of the 2 predictors, Gest or Weight, is a better predictor of Height?A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…
- A distribution with µ = 55 and o = 6 is being standardized so that the new mean and standard deviation will be u = 50 and o = 10. When the distribution is standardized, what value will be obtained for a score of X= 58 from the original distribution?7. Suppose a teacher looks at a random sample of 42 final exam completion times and finds a mean timeof 111 minutes with asamplestandard deviation of 44 minutes. Which equation should they use tocompute the margin of error?A.E=s√nB.E=z√pqnC.E=zs√nD.E=ts√nE.E=t√pqn 8. Suppose a teacher looks at a random sample of 42 final exam completion times and finds a mean timeof 111 minutes with asamplestandard deviation of 44 minutes. Which value best approximates themargin of error for a 95% confidence interval?A.E= 6.8B.E= 33.4C.E= 13.3D.E= 13.7E.E= 34.4 9. A TWISTER spinner has four outcomes; red, blue, yellow, green. Tim believes that the proportion ofred outcomes is not equal to 25%. Which of the following correctly depicts hisnull hypothesis,H0?A.H0:μ >25B.H0:μ= 25C.H0:μ <25D.H0:μ6= 25E.H0:p=.25F.H0:p > .25G.H0:p < .25H.H0:p6=.25Page 2 10. A TWISTER spinner has four outcomes; red, blue, yellow, green. Tonya tests the claim that theproportion of red…Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin, - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team===== "Brooklyn Nets" . Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1459.95122 1 80 190.65061 None of the above 81 206.320988 Coef. Std. Err. 8.439024 3.049595 -5.219512 2.156389 MS t Number of obs F(1, 80) Prob > F R-squared O The Nets lost more games than they won in 2014 P>|t| 2.77 0.007 -2.42 0.018 Adj R-squared = Root…
- 4. Suppose you are given the following information: = 49.6870 – 2.1586X; r2 = 0.9757 (0.7463) (0.12113) df=8 T= (66.578) (-17.821) p-value = (0.000) (0.000) a) Conduct a two tailed hypothesis test that: i) The intercept is 49 and the slope coefficient is -2, use 1% significance. ii) Confirm your deductions to 4(a) (i) using a confidence interval approach b) What does the r2 tell you? c) Perform a hypothesis using r2, such that p=D0, what do you conclude?The mean daily energy requirement for eight-year-old boys is 2200 calories. An education researcher believes that many students in this group do poorly in school due to an inadequate diet and not having enough energy. A random sample of academically at-risk eight-year-old boys was obtained, and their caloric intake was carefully measured for a day (1 day). The summary statistics were n = 37 X = 2089. Assuming o = 358, A) Is there any evidence that this group of students has a mean caloric intake below the daily average requirement? Make use of o = 0.05 (i) Define the parameter of interest to the researcher (ii) State the Null and Alternative Hypothesis (iii) What test statistic would you make use of and why? Justify, with reasons. (iv) Compute the value of the test statistic. (v) Rejection Region: (vi) Determine p-value for the test. (vii) Conclusion and decision:If the life expectacy in county A is 65 years with CI of (55, 75) and in county B is 87 years with CI of (40, 98), are the two life expectancies likely to be statistically different?
