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- A researcher conducts a hypothesis test using a sample from an unknown population. If df = 30 for the t-statistic and M = 46 and s2 = 10, how many individuals were in the sample?Use software or Table C to find the critical value t∗ corresponding to the middle 98% of the t(21) distribution. the critical value t∗ with area 0.025 to the right of t∗ under the t(24) distribution. the area under the t(5) distribution to the right of t=3.A metal rod of length L and a sphere of radius R are to be joined to form a small automobile part. L and R are normally distributed with the following parameters: E(L) = 2cm, E(R) = 0.5cm, V(:) =0.1^2 cm, V(R)=0.05^2 cm^2. Assume that L and R are independent. What is the probability that the total length of a single assembly is less than 2.90 cm?
- Given the moment generating function MX(t) = e 3t+8t2 , find the moment generating function of the random variable Z = 4(X − 3), and use it to determine the mean and the variance of Z.From this geometruc distrubtion. (0.45)8(0.55). What does the 8 represent? 1. Probability of failure 2. Probability of success 3. The number of failurees 4. Number of sucessesA marketing research group found that 25% of the 200 shoppers, it recently interviewed at a certain shopping center, resided more than 12 miles from the center. Assume that a random sample was taken, construct a 95% C.I. for the actual; percentage of shoppers who live more than 15 miles from that center.
- Consider X and Y are joint distributed with PDFf(x,y)=x+y, 0≤x≤1, 0≤y≤1. (a) Find the probability that X > 0.5. (b)FindP(X> Y 1/2).(c) Are X and Y independent?Using the Laplace Principle of Indifference to know the uncertainty, solve the following; In a tour to outside, we have 40 times food trip, 25 times clothing and 15 times grocery visits to a same place. If we extract to plan a random visit, what is the probability of having A food trip only? A clothing with half the chance of food but not grocery? A grocery with no food and clothing?Given the MGF of X is MX(t)=(0.90+0.10et)10MX(t)=(0.90+0.10et)10 . Clearly; i) Find the probability P(X=1), ii) Find the probability P(X=2), iii) Find the probability P(X≤2)P(X≤2). Also use the working in this question to answer the following three questions
