Compute expected frequencies scIs the lottery fair? Powerball is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the ballsdrawn is the "Powerball." Matching the number drawn on the Powerball increases one's winnings. In a 17 month period, the Powerball was drawn from acollection of 35 balls numbered 1 through 35. A total of 149 drawings were made. For the purpose of this exercise, we grouped the numbers in to fivecategories: 1-7, 8-14, and so on. If the lottery is fair, then the winning number is equally likely to occur in any category. Following are the observed frequencies.Test the hypothesis that each of the categories is equally likely. Use the 0.05 level of significance and the critical value method with the table.Category 1-7 8-14 15-21 22-28 29-35Observed 26 40 28 34 21Send data to ExcelPart: 0/7Part 1 of 7Compute the expected frequencies.CategoryExpected frequencySkip PartF1B-Check-0²F21-7 8-14 15-21 22-28 29-3520F3AUG11DOODOOF49/XF5$MacBook AirF6&F7► 11*FBSubmit AssignmentⒸ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | AccessibilityBtvSave For LaterF9CEspeF10←E4Vdo5

Given that Observed Frequency and Expected Frequency table Category 1-7 8-14 15-21 22-28 29-35…

Answered: Is the lottery fair? Powerball is a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. Let X1, X2, ..., Xn be a random sample from the population N(µz,0²) and Y1, Y2,...,Ym a random sample from the population N(µy, o2), where both means (z and Hy) are assumed known. Note that the two distributions have a common variance of o². (a) If the X's and Y's are independent, show that the MLE for the common variance is: E (Xi - H2)² +E(Y; - Hy)? n+ m (b) Is the MLE found above unbiased for o2?
The arrival rate of patients at a hospital counter follows Poisson distribution with a mean of 25 per hour. The service rate of the treatment to patients also follows Poisson distribution with a mean of 45 per hour.d) Find Ls, Lq, Ws and Wq
The number of vehicles arriving at a toll booth, per minute, were observed as follows: 0, 3, 1, 2, 0, 1, 1, 1, 2, 0, 1, 4, 3, 1, 1, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0 (1) Assuming that the arrival rate of vehicles at the toll booth is a Poisson process, estimate the mean arrival rate using the method of moments. (2) Perform a chi-square test to determine the validity of the Poisson distribution at the 1% significance level.
Suppose the log-ins to a company's computer network follow a Poisson process with an average of three counts per minute. What is the mean time between counts? What is the standard deviation of the time between counts?
An investigator analyzed the leading digits from 794 checks issued by seven suspect companies. The frequencies were found to be 218, 130, 106, 83, 65, 48, 48, 37, and 59, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.025 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? Leading_Digit Actual_Frequency Benford's_Law:1) 218 30.10%2 )130 17.60%3) 106 12.50%4) 83 9.70%5) 65 7.90%6) 48 6.70%7) 48 5.80%8) 37 5.10%9) 59 4.60% Calculate the test statistic, χ2 =? (Round to three decimal places as needed.) Calculate the P-value=? (Round to four decimal places as needed.)
find the p-value for two tailed z test if test statitic is 2.5
Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. a What percentage of time all dispatchers are idle? b What percentage of time only one dispatcher is busy? c. What is the average number of callers in the system? d What is the average time in minutes that a customer spends in the system? e What is the total cost of the system for 8 hours if each dispatcher charges $25 /hour and the waiting cost per hour for…

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