(a) What are the null hypothesis H, and the alternative hypothesis H, that themanagers should use for the test?Ho:H: 0(b) What is the probability that the managers commit a Type I error? Round yourresponse to two or more decimal places.(c) Assuming that the actual value of u is 41.2 minutes, what is the probability thatthe managers reject the null hypothesis? Round your response to two or moredecimal places.(d) Suppose that the managers decide to perform another statistical test using thesame population, the same null and alternative hypotheses, and the same samplesize, but for this second test the managers use a significance level of 0.1 insteadof a significance level of 0.01. Assuming that the actual value of u is 41.2 minutes,how does the probability that the managers commit a Type II error in this secondtest compare to the probability that the managers commit a Type II error in theoriginal test?O The probability of committing a Type II error in the second test is greaterO The probability of committing a Type II error in the second test is lessOThe probabilities of committing a Type II error are equal Managers at an automobile manufacturing plant would like to examine the mean completion time u for an assembly line operation. The past data indicate thatEspañolthe mean completion time is 40 minutes, but the managers have good reason to believe that this value has increased. The managers plan to perform astatistical test of the claim and choose a random sample of 75 completion times in preparation for this test.Suppose that the population of completion times for the assembly line operation has a standard deviation of 3 minutes and that the managers perform theirhypothesis test using the 0.01 level of significance.Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses asindicated.(If necessary, consult a list of formulas.)

Dear students as per the guidelines we solve only first three subparts only multiple parts are…

Answered: (a) What are the null hypothesis H, and…

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 personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, µ, on this subsection among the general population. You decide that you'll use the mean of a random sample of scores on this subsection to estimate u. What is the minimum sample size needed in order for you to be 90% confident that your estimate is within 3 of u? Use the value 23 for the population standard deviation of scores on this subsection. Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)
11
A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, μ, on this subsection among the general population. You decide that you'll use the mean of a random sample of scores on this subsection to estimate μ. What is the minimum sample size needed in order for you to be 90% confident that your estimate is within 3 of μ? Use the value 23 for the population standard deviation of scores on this subsection. Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
3. An airline has a baggage weight limit of 50 lb. Suppose that the weight of the baggage checked by an individual passenger is a random variable x with a mean value of 49 lb. If 110 passengers will board a flight, what is the approximate probability that the mean weight for this sample of passengers will exceed the limit if the standard deviation of the baggage weight for this group is 23 lb. ? (Round your answer to three decimal places.)
You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.67. Your sample data produce the test statistic z=3.203. Find the p-value accurate to 4 decimal places. You are conducting a study to see if the probability of catching the flu this year is significantly different from 0.33. Your sample data produce the test statistic z=1.84 Find the p-value accurate to 4 decimal places.
18. With respect to the chi-square test, a p value of 0.034 means there is a 3.4% probability that the deviation of the observed value from the expected value is due to chance and a 96.6% probability that this is not due to chance. True False
Researchers developed a "cat IQ test" and find that the population of cats in the United States has a mean score of u = 25 on this test with a standard deviation of g = 3. You decide to test a sample of n = 45 cats to do some research about whether some breeds are smarter. You collect your sample of n = 45 cats and find their mean cat IQ is M = 25.5. What is the probability of this sample? That is, what is p(M>25.5)?
For any problem where you use a preprogrammed TI function, you must write down which function you use (complete name, not just something like "normal" because there are multiple normal functions), what values you enter (in order), and what the calculator produces. Round all probabilities to at least four decimal places. According to an article in the Journal of Anatomy (May, 2013), the ratio of the length of a person's femur to the length of their tibia averages 1.23. Suppose this ratio is approximately normal with a mean of 1.23 and a standard deviation of sigma C. What proportion of people have a ratio between c1 and c2? e1 f1 3.564 6.1875 sigma 0.031 b1 1.25 c1 1.2187 c2 1.266 d1 90 beta 4.95 f2 14.058 g1 25.7 g2 70.9 h1 33.47 h2 58.06
A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 5 inches. A random sample of 41 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 35 and standard deviation ? = 10. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60 (b) x is greater than 16 (c) x is between 16 and 60 (d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

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