3.6.9. Let F have an F-distribution with parameters ri and r2. Argue that 1/F has an F-distribution with parameters r2 and r1.
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- Which statement is not consistent with the distribution of f ratios? F values that make up the f ratio distribution are always positive With very large sample sizes, f ratios tend to be clustered close together With very small sample sizes, f ratiosbtend to be more spread out With large sample sizes, f ratios are clustered around 0A pharmcuticle company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of Mercury) for 9 patients before taking the new drug and 2 hours after taking the drug are shown in the table below. is there enough evidence support the company's claim? Let D =(blood pressure before taking new drug)- (blood pressure after taking new drug).use significant levels of a=their 0.05 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patience both Before & After taking the new drug. 1.State the null and alternative hypothesis for the test. 2. Find the value of the standard deviation of the paired differences. Round to one decimal place. 3.compute the value of the test statistic. Round to three decimal places 4.determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion to three decimals. 5.make decision for the hypothesis test.Suppose that at a gas station the daily demand for regular gasoline is normally distributed with a mean of 1000 gallons and a standard deviation of 100 gallons. The station manager has just opened the station for business and there is exactly 2300 gallons of regular gasoline in storage. The next delivery is scheduled later tomorrow at the close of business. (a) Let X1 and X2 denote the demand of today and tomorrow, respectively. Let X = X1 + X2. Find the distribution of X. (b) Find the probability that the manager will have enough regular gasoline to satisfy today’s and tomorrow’s demand.
- Suppose we claim that the average GPA for all students at a University is less than 2.9. From a sample of 15 students, the average GPA is 2.85 with a standard deviation of 1.6. The GPAʹs are normally distributed and α = 0.05. Choose the appropriate decision rule below. A) Reject H0 if t > 1.761 B) Reject H0 if t < -2.145 C) Reject H0 if t < -1.761 D) Reject H0 if z < -1.645 E) Reject H0 if z > 1.645Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.Suppose that f (x) = (3/2)x2 for −1< x < 1. Determine the mean and standard deviation of X.
- In a sample of 14 randomly selected high school seniors, the mean score on a standardized test was 1197 and the standard deviation was 164.9. Further research suggests that the population mean score on this test for high school seniors is 1022. Does the t-value for the original sample fall between - to 95 and to o5? Assume that the population of test scores for high school seniors is normally distributed. The t-value of t= V fall between - to 95 and to 95 because to g5 =. (Round to two decimal places as needed.)Suppose the variables Q and W are skewed distributions defined over a limited set of values. What is the probability that Q takes on a value between ½ and 1? What is E(Q)?If X1, X2, ... , Xk have the multinomial distribution of Definition 8, show that the mean of the marginal distribu-tion of Xi is nθi for i = 1, 2, ... , k.
