Determine the distribution of Xn for the following Let X1, X2.....X15 be a random sample from Bin (10, ²)
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- Let A1, A2, . . . , A100 be a random sample from a uniform distribution on the interval(0,1). Let B = A1 + A2 + . . . + A100. 1. Let A¯ = B/100. Find P(2 < A¯ < 2.15).The average wait time to get seated at a popular restaurant in the city on a Friday night is 11 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 15 randomly selected men who were wearing a tie are shown below Assume that the distribution of the population is normal. 11,9,9, 12, 11, 10, 12, 13, 9,9, 11, 13, 12, 9,9 What can be concluded at the the α 0.01 level of significance level of "-? S1 canc a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: C. The test statistic ? ' - please show your answer to 3 decimal places.) d. The p-value = Please show your answer to 4 decimal places.) e. The p-value is?a f Based on this, we should Select an answer g Thus, the final conclusion is that the null hypothesis. The data suggest the populaton mean is significantly more than 11 at a = 0.01, so there is statistically significant evidence to conclude that the population mean wait time for men who wear a tie is more than 11…7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)
- Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)34. Suppose that X is a random variable with MGF M(t) = (1/8)e + (1/4)e + (5/8)e. (a) What is the distribution of X? (b) What is P[X= 2]?5. Let (Xi, Yi), i 1, 2, ,n, be a random sample from a bivariate normal distribution. Find the joint distribution of (X,Y).
- Suppose that the time. in days, required to repair a heat pump is a random variable X having a gamma distribution with parameters k = 8 and A = 2. What is the probability that on the next service call (a) at most 3 day will be required to repair the heat pump? (b) at least 2 days will be required to repair the heat pump? %3D %3DA manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following (refer Table 4): Employees y X1 X2 1 100 9 6 2 90 4 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 2 4 8 30 2 2 (a) Run a regression analysis based on the data in Table 4 using Mic. Office EXCEL. Based on theoutput, propose a regression equation that can be used to predict paralegal GPA.(b) Interpret the coefficient value of each independent variable in the constructedmodel(c) Is each independent variable sharing a significant linear relationship with the dependent variable?Verify at 0.05 level of significance. Make your conclusion based on the p-value in the EXCEL output.The average wait time to get seated at a popular restaurant in the city on a Friday night is 10 minutes. Is the mean wait time less for men who wear a tie? Wait times for 15 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 7, 10, 11, 9, 11, 7, 8, 11, 9, 9, 11, 9, 11, 9, 7 What can be concluded at the the α = 0.10 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H0: H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly less than 10 at α = 0.10, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is equal to 10.…