8 Julia is waiting for either of the two buses to her destination, and waiting times for those two different buses follow independent exponential distributions with mean 3 minutes and 7 minutes. Assuming she would get on the bus that comes first, what is her expected waiting time?
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- Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with A = 0.0003. • What proportion of the fans will last at most 10,000 hours? • What proportion of the fans will last at least 7000 hours? a. 0.0498, 0.8775 Ob. NONE Oc 0.0498, 0.1225 Od.0.0502, 0.1225Suppose the observational units in a study are the patients arriving at an emergency room on a given day, 11 Nov 2019. For the following indicate whether it can legitimately be considered a variable or not: Whether or not men have to wait longer than women yes noWhat is indicated by a Pearson correlation of r= +1.00 between X and Y? O Every increase in X causes an increase in Y Every change in X causes a change in Y O Each time X increases, there is a perfectly predictable increase in Y All of the other 3 choices occur with a correlation of +1.00.
- A world wide fast food chain decided to carry out an experiment to assess the influence of income on number of visits to their restaurants or vice versa. A sample of households was asked about the number of times they visit a fast food restaurant (X) during last month as well as their monthly income (Y). The data presented in the following table are the sums and sum of squares. (use 2 digits after decimal point) ∑ Y = 393 ∑ Y2 = 21027 ∑ ( Y-Ybar )2 = SSY = 1720.88 ∑ X = 324 ∑ X2 = 14272 ∑ ( X-Xbar )2 = SSX = 1150 nx=8 ny=11 ∑ [ ( X-Xbar )( Y-Ybar) ] =SSXY=1090.5 PART A Sample mean income is Answer Sample standard deviation of income is Answer 90% confidence interval for the population mean income (hint: assume that income distributed normally with mean μ and variance σ2) is [Answer±Answer*Answer] 90% confidence interval for the population variance of income (hint: assume that income distributed normally with mean μ and variance σ2) is…You were asked to help with an analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers’ AGE at birth (continuous variable in years), mothers’ current HOUSING status (“own” and “not-own”; “own” is the reference group), and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “Staten Island”; “Manhattan” is the reference group). Write down the population model that estimates the effect of mother’s AGE on BW while adjusting for mother’s current HOUSING status. If you use dummy or binary variables, specify what they mean. Write down the population model that estimates the effect of mother’s AGE on BW while adjusting for mother’s current HOUSING status and BOROUGH. If you use dummy or binary variables, specify what they mean. Write down the population model that estimates the effect of mother’s AGE…Please use excel formulas when possible: You have a device that uses a single battery, and you operate this device continuously, never turning it off. Whenever a battery fails, you replace it with a brand new one immediately. Suppose the lifetime of a typical batteryhas an exponential distribution with mean 205 minutes. Suppose you operate the device continuously for three days, making battery changes when necessary. Find the probability that you will observe at least 25 failures. (Hint: The number of failures is Poisson distributed.) In the previous problem, we ran the experiment for a certain number of days and then asked about the number of failures. In this problem, we take a different point of view. Suppose you operate the device, starting with a new battery, until you have observed 25 battery failures. What is the probability that at least 15 of these 25 batteries lived at least 3.5 hours? (Hint: Each lifetime is exponentially distributed
- b. The lifetime X of a particular species is assumed to be exponentially distributed with mean 75 time units. Find the probability that a member of this particular species picked at random survives: i. more than 90 time units; less than 70 time units; between 70 and 85 time units. ii. iii. iv. Calculate Var(X).If N = 150, (A) = 93, (B) = 112, (C) = 80, (BC) = 20 and (Ay) = 43, find the greatest and the least possible values of (AB) so that the data may be consistent.Please solve it perfectly
- 5. You have a sample of 19 students and plan to determine if a linear relationship can be used to predict the SAT score as a function of the high school GPA. What value does the correlation coefficient need to exceed, according to the r√n> 3 rule, in order for you to be able to say that the correlation between the SAT score and the high school GPA is significant, instead of it having occurred by random chance? Write your answer as a decimal correctly rounded to three decimal places.Suppose you are interested in the role of social support in immune function among retired men who live alone. You ask 50 patients to record the number of days they do not see or interact with a friend or family member over a period of 1 month to see whether the number of nonsocial days in a typical month correlates with the number of new illnesses they experience per year. You decide to use the computational formula to calculate the Pearson correlation between the number of nonsocial days in a month and the number of illnesses per year. To do so, you call the number of nonsocial days in a month X and the number of illnesses per year Y. Then, you add up your data values (∑X and ∑Y), add up the squares of your data values (∑X2 and ∑Y2), and add up the products of your data values (∑XY). The following table summarizes your results: ∑X 590 ∑Y 380 ∑XY 4,887 ∑X2 10,456 ∑Y2 4,258 Find the following values: The sum of squares for the number of nonsocial days in a month is SSX=…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…
