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- PLEASE ANSWER: E, F & GThe calibration of a scale is to be checked by weighing a 11 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ho: H = 11 Ha: u + 11 Ho: H + 11 H3i H 11 a (b) With the sample mean itself as the test statistic, what is the P-value when x = 10.83? (Round your answer to four decimal places.) What would you conclude at significance level 0.01? Conclude that the true mean measured weight differs from 11 kg. Conclude that the true mean measured weight is the same as 11 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 11.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 10.9? (Round your answer to…State whether the standardized test statistic t indicates that you should reject the null hypothesis. Explain. (a) t =1.667 (b) t =0 (c) t= -1.552 (d) t= -1.705 (look at image below)
- The time it takes to drive from Austin to Bastrop depends on the route taken: Probability of Travel time|Route Route Taking Route (in minutes) 90% Normal(u = 60, o = 5) HWY 71 MLK 8% Uniform[55, 75] 95 to 270 2% Exponential(mean= 65) Let T denote the travel time between Austin and Bastrop. Determine Var[T]. 1. Less than 80 minutes. 2. At least 110, but less than 120 minutes. 3. At least 80, but less than 100 minutes. 4. At least 120 minutes. 5. At least 100, but less than 110 minutes.2.4The probability mass function of a discrete random variable Y is given by k y = 2, 3,4, 5 p(y) = { 6- y 0, PV) : elsewhere
- 4. An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having pmf 0.9 f(x) = x = 0 x = 1,2,3,4,5,6 where c is a constant. a) Find c. b) Find the expected value of the amount the insurance company must pay.Given Y it = B 0 + B 1Treated i + B2After t + B3(Treated i*After t) + e it, the expected value of the dependent variable for those who in the control group after the treatment was administered is: A. B0 + B1 + B2 + B3 B. B0 + B2 C. B0 + B1 D. B0 + B1 + B3Let X be the total amount saved in dollars at the cash register. The pdf of X is given by: Value of X 20 28 40 50 58 70 probability 0.36 0.21 0.24 0.1225 0.0175 0.03 .0175 0.0025 Before I make the purchase, you would place my chance of saving $20 at 24%. Suppose you approach me after I pay for my items and ask: "Did you save any money?" If I answer "no", then you know I didn't save $20 and thus the chance of saving $20 changes from the unconditional chance 24% to the conditional chance 0%. However, if I answer "yes" my chance of saving $20 would get higher. What would be the conditional chance of saving $20 if you knew I got a discount? Mathematically, we seek: P(X = 20|X > 0 ). Even though it looks weird, it is just a conditional probability. Find it. P(X = 20|X > 0) = P(X = 20 and X > 0) / P(X > 0) = Hint: P(X = 20 and X > 0) be read off the table by identifying possible values where the event (X = 20 and X > 0) is true, don't use the multiplication rule. Do not round, express your…