The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a nullhypothesis are given in parentheses. Compute the x²-test statistic, and use the x²-distribution to find the p-value of the test.chi-square statistic = iCategoryObservedp-value =(Expected)A139(160)B188(160)с45(40)DRound your answer for the chi-square statistic to two decimal places, and your answer for the p-value to four decimal places.28(40)

Answered: The categories of a categorical…

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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A district ofﬁcial intends to use the mean of a random sample of 900 sixth graders from a very large school district to estimate the mean score that all the sixth graders in the district would get if they took a certain arithmetic achievement test. The official knows that σ=9.4 for such data. Suppose that the district ofﬁcial takes her sample and gets x=61.8. Use the above variance formula to construct a 99% conﬁdence interval for the mean score of all the sixth graders in the district.
Most individuals are aware of the fact that the average annual repair cost for an automobiledepends on the age of the automobile. a researcher is interested in finding out whether thevariance of the annual repair costs also increases with the age of the automobile. a sampleof 26 automobiles 4 years old showed a sample standard deviation for annual repair costsof $170 and a sample of 25 automobiles 2 years old showed a sample standard deviationfor annual repair costs of $100.a. state the null and alternative versions of the research hypothesis that the variance inannual repair costs is larger for the older automobiles.
Most individuals are aware of the fact that the average annual repair cost for an automobiledepends on the age of the automobile. a researcher is interested in finding out whether thevariance of the annual repair costs also increases with the age of the automobile. a sampleof 26 automobiles 4 years old showed a sample standard deviation for annual repair costsof $170 and a sample of 25 automobiles 2 years old showed a sample standard deviationfor annual repair costs of $100.a. state the null and alternative versions of the research hypothesis that the variance inannual repair costs is larger for the older automobiles.b. at a .01 level of significance, what is your conclusion? what is the p-value? Discussthe reasonableness of your findings.
Suppose that the fraction of defective modems shipped by a data-communications vendor has an approximation beta distribution with a=5 and b=21. find the mean and variance of the fraction of defective modems per shipment What is the probability that a randomly selected shipment will contain at least 30 % defectives? What is the probability that a randomly selected shipment will contain no more than 5 % defectives?
The mean weight of luggage checked by a randomly selected tourist-class passenger flying between two cities on a certain airline is 40 lb. and the standard deviation is 10 lb. The mean and standard deviation for a business-class passenger are 30 lb. and 6 lb, respectively.a. If there are 12 business-class passengers and 50 tourist-class passengers on a particular flight, what are the expected value of total luggage weight and the standard deviation of total luggage weight?b. If the individual luggage weights are independent, normally distributed rv’s, what is the probability that total luggage weight is at most 2500 lb?
American Theatre owners knew that a certain hit movie ran an average of 84 days or more in each city, and the corresponding deviation is 10 days. The manager of the south-eastern district is interested in comparing the movies popularity in his region with that in all of American’s other theatres. He randomly chose 25 theatres in his region and found that they ran the movie on an average of 81.5 days. Test this claim at α = 0.05 level of significance. Population mean μ = 84 days Sample mean x̅ = 81.5 days Population standard deviation σ = 10 days Sample size n = 75 1. State the null and alternative hypothesis. Ho: = 84 Ha: ≠ 84 2. At 95% confidence level, what is the level of significance? 3. Determine what type of test to use and determine the critical value. 4. Calculate the test statistic using the appropriate formula. 5 .Compare the calculated test statistics with that of the critical value. 6. Make a decision. 7. Interpret the result.
The mean weight of a fire ant worker is 3.11 mg with a standard deviation of .49 mg. The mean weight of a carpenter ant worker is 3.02 mg with a standard deviation of .35 mg. Let F be the weight, in mg, of a randomly selected fire ant worker. Let C be the weight, in mg, of a randomly selected carpenter ant worker. It is known that weights of all ants are normally distributed. F and C are independent. What is the probability that randomly selected fire ant worker weighs between 2.95 and 3.07 mg.? What is the 95th percentile of the distribution of F? What is the median of the distribution of F-C ? What is the probability that both F and C are greater than 3 mg. ? What is the probability that F is greater than C?
Of a large stockpile of used pumps, 20% are unusable and need repair. Arepairman is sent to the stockpile with three repair kits. He selects pumps at random and tests them one at a time. If a pump works, he goes on the next one. If a pump doesn’t work, he uses one of his repair kits to fix it. Suppose it takes 10 minutes to test a pump and 20 minutes to repair a pump that doesn’t work. Find the mean and standard deviation of the total time it takes the repairman to use up his three kits.
The actual weight of a bag of flour is modeled as a normal random variable with a mean of 0.25 kilograms (kg) and a standard deviation of 0.02 kg. A sack of flour is considered ready-to-ship if its weight is between 0.24 kg and 0.27 kg. Consider a sample of 50 sacks of flour. Assume that the weights of the individual sacks in the sample are independent. a) What is the probability that an individual sack of flour in the sample will have a weight between 0.23 kg and 0.27 kg? b) What is the probability that the average weight of the sacks of flour in the sample of 50 will be between 0.23 kg and 0.27 kg?

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