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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- 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…10 veterans who suffer from PTSD are tested before and after taking an anti-anxiety medication thought to reduce PTSD symptoms. How do I report my findings in APA format? Before condition (M=52, SD= 13.4, SE=4.228) After condition (M=43, SD=13.4, SE=4.243) t(9)=1.581, p >0.05, d=0.500.7. 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…
- a. What is the probability that it would take more than 4 minutes to reach the accident? b. What is the probability that it would take either less than 2 minutes or more than 5 minutes to reach the scene of the accident? c. What is the expected time to reach the accident?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?
- Albumin is a liver protein that helps circulate vitamins throughout the body. Reduced Albumin has been associated with severe illness with Covid-19 patients. Suppose we wanted to conduct a study to compare the mean Albumin concentration (g/L) between a sample of adult patients hospitalized for Covid 19 (Sample Mean= 32.8, s=6.0) to the mean albumin concentration (g/L) of healthy adults (u=34.1, o=7.13). How many patients would need to enroll from the hospital to conduct this study with 99% confidence, and 80% power? A. 267 B. 120 C. 352 D. 225If 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?Model the following data with a power formula. x 1 2 3 4 5 y 1 1/8 1/27 1/64 1/25 a) x^-3 b) x^-4 c) x^3 d) x^4
- (c) A factory produces two types of artificial lamp A and B. The mean durability of artificial lamp A is 850 hours and its standard deviation is 40 hours. While, mean durability of artificial lamp B is 820 hours and its standard deviation is 60 hours. Find the probbality of 35 artificial lamp A will have mean durabilirty at least 25 hours more than 45 artificial lamp B.A correlation coefficient might not have an appropriate relationship between two variables. This can happen between two variables when A. it is highly scattered B. is nonlinear is some way C. has a directionality problemn,T 3. Suppose {uit}i=1,t=1 be i.i.d. variables with mean zero and variance o?. Show that for each i, Auit is autocorrelated. That is, Auit is correlated to some of its past values. E.g., it is enough to calculate Cov (Auit, Auit-1) and Cov (Auit, Auit-2) to see if any of these are non-zero.
