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Take Test: fall 2023 ±nal exam multiple choice Test Information Description Instructions Timed Test This test has a time limit of 1 hour and 10 minutes.This test will save and submit automatically when the time expires. Warnings appear when half the time , 5 minutes , 1 minute , and 30 seconds remain. Multiple Attempts Not allowed. This test can only be taken once. Force Completion Once started, this test must be completed in one sitting. Do not leave the test before clicking Save and Submit . Your answers are saved automatically. QUESTION 1 What are the mean and variance of a standard normal distribution? 1; 0 1; 1 0; 1 0; 0 3 points Save Answer QUESTION 2 Suppose we will take a random sample of size n=40 from a population (with normal distribution) having mean 6 and variance 16. What is the standard deviation of the sample mean? a. 40; b. 2.52; 3 points Save Answer Question Completion Status: Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

c. 4; d. 0.63; e. 0.4 a b c d e QUESTION 3 A special advertising section in the July 20, 1998, issue of Fortune magazine discusses “outsourcing.” According to the article, outsourcing is “the assignment of critical, but noncore, business functions to outside specialists.” This allows a company to immediately bring operations up to best-in-world standards while avoiding huge capital investments. Assume that 40 percent of all business executives feel that the benefits of outsourcing are either more or much more than expected. You randomly select 10 business executives. Let X be the total number of business executives who DO NOT feel that the benefits of outsourcing are either more or much more than expected. What is P(X=3)? a. 0.0425; b. 0.9936; c. 0.9672; d. 0.9991; e. 0.0008 a b c d e 3 points Save Answer QUESTION 4 A group consists of 6 men and 6 women. Four people are selected to attend a conference. In how many ways can 4 people be selected from this group of 12? In how many ways can 3 men and 1 woman be selected from the group? Find the probability that the selected group will consist of 3 men and 1 women. (choose 495; 16; 16/495 ) 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

495; 225; 225/495 330; 225; 225/330 495; 16; 16/495 330; 200; 20/33 330; 250; 25/33 QUESTION 5 Recall that the cigarette industry requires that models in cigarette ads must appear to be at least 25 years old. Also recall that a sample of 50 people is randomly selected at a shopping mall. Each person in the sample is shown a “typical cigarette ad” and is asked to estimate the age of the model in the ad. The sample gives a mean of 23.663 years and a standard deviation of 3.596 years. Let µ be the mean perceived age estimate for all viewers of the ad, and suppose we consider the claim that µ is at least 25. Please test the claim at α=0.01. Assume population σ=3.596. Please set up the hypothesis testing a. H 0 :µ≥25 H a :µ<25; b. H 0 :µ≤25 H a :µ>25; c. H 0 :µ=25 H a :µ≠25; d. H 0 :µ≠25 H a :µ=25; e. H 0 :µ<25 H a :µ≥25 a b c d e 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

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QUESTION 6 For the above problem, the test statistic is a. -18.5901; b. 2.629; c. 18.5901; d.1.648; e. -2.629 a b c d e 3 points Save Answer QUESTION 7 What is the p-value? a. 0.9557; b. 0.0043; c. 0.00215; d. 0.0086; e. 0.0495 a b c d e 3 points Save Answer QUESTION 8 An individual who has automobile insurance from acertain company is randomly selected. Let Y be thenumber of moving violations for which the individualwas cited during the last 3 years. The pmf of Y is y p(y) 0 0.5 1 0.25 2 0.20 3 0.05 Suppose an individual with Y violations incurs a h f $ 150 2 C l l t th t d 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

surcharge of $ 150 Y 2 . Calculate the expected amount of the surcharge. 1.5 15 50 75 225 QUESTION 9 A battery company developed a new product. Quality engineers found that the life times of the new batteries have a normal distribution with mean 40000 minutes and variance 5000 minutes. To attract new customers, the battery company will give customers full refund if the purchased batteries do not last longer than the minutes stated in the guarantee of the new battery. What is the guaranteed minutes if the battery company expects that 2 percent of the customers who purchase the new batteries will be eligible for full refund? 32160 30680 51650 28350 39855 3 points Save Answer QUESTION 10 A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs and 24 lbs respectively then 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, by central limit theorem the probability that the total weight of the boxes will not exceed 2952 lbs. is: 0.0013 0.9722 0.0228 0.9987 0.1587 QUESTION 11 A random-number generator is supposed to produce a sequence of 0s and 1s with each value being equally likely to be a 0 or a 1 and with all values being independent. In an examination of the random- number generator, a sequence of 50,000 values is obtained of which 25,264 are 0s. Formulate a set of hypotheses to test whether there is any evidence that the random-number generator is producing 0s with probability 0.5. Please find the p- value. ( choose 0.0182 ) 0.0096 0.0094 0.0089 0.0182 0.0193 3 points Save Answer QUESTION 12 A random-number generator is supposed to produce a sequence of 0s and 1s with each value being equally likely to be a 0 or a 1 and with all values being independent. In an examination of the random- number generator, a sequence of 50,000 values is obtained of which 25,264 are 0s. 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

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Formulate a set of hypotheses to test whether there is any evidence that the random-number generator is producing 0s and 1s with unequal probability at significance level of 0.01. Based on your test result, what is you conclusion. There is evidence that the random number generator is generating equal proportions of 1s and 0s . There is strong evidence that the random number generator is generating equal proportions of 1s and 0s . There is no enough evidence that the random number generator is generating unequal proportions of 1s and 0s . There is strong evidence that the random number generator is generating unequal proportions of 1s and 0s . QUESTION 13 For a two sample problem with n=40 paired samples, z i = x i − y i , where x i is f or population A and y i is f or population B . If the mean of Zi is -2.655 and the standard deviation is 3.730. Please perform the paired t-test for H a : μ A = μ B . what is the test statistic of the problem? 4.50 -4.50 4.45 -4.45 -6.37 3 points Save Answer QUESTION 14 For a two sample problem with n=40 paired samples, z i = x i − y i , where x i is f or population A and y i is f or population B . 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

If the mean of Zi is -2.655 and the standard deviation is 3.730. Please perform the paired t-test for H a : μ A ≠ μ B . Please estimate the range of the p-value. >0.1 between 0 . 0 5 and 0.1 between 0 . 0 1 and 0.05 between 0 . 0 0 1 and 0 . 0 1 below 0.001 QUESTION 15 Suppose x=21 is an observation from a binomial random variable B(27, p) random variable with certain p. Compute a two sided 95% interval for p. Hint: use the formula for Two-Sided Confidence Intervals for a Population Proportion (0.572, 0.984) (0.621, 0.935) (0.591, 0.964) (0.646, 0.909) (0.625. 0.705) 3 points Save Answer QUESTION 16 Die A is rolled 50 times and a 6 is scored 14 times, while a 6 is obtained 20 times when die B is rolled 100 times. Construct a two-sided 98% confidence interval for the 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

Construct a two sided 98% confidence interval for the difference in the probabilities of scoring a 6 on the two dice. Hint: use the formula for Confidence Intervals for the Difference of Two Population Proportions (0.004953348, 0.1550467) ( -0.04345174, 0.2034517) ( -0.09278989, 0.208765488) (-0.06709144, 0.2270914) (-0.0948587, 0.2548587) QUESTION 17 Die A is rolled 50 times and a 6 is scored 14 times, while a 6 is obtained 20 times when die B is rolled 100 times. Calculate the test statistics for the two-sided null hypothesis that the two dice have equal probabilities of scoring a 6. 0.8536 0.9554 -1.729 2.232 1.1032 3 points Save Answer QUESTION 18 Die A is rolled 50 times and a 6 is scored 14 times, whilea 6 is obtained 20 times when die B is rolled 100 times. Calculate a p-value for the two-sided null hypothesis that the two dice have equal probabilities of scoring a 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

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6. 0.0456 0.0371 0.0909 0.1357 0.2713 QUESTION 19 In an unpaired two-sample problem an experimenter observes n=18, mean x = 32.45, variance s 2 x = 4.3 , from population A, and m=21, mean ⎯⎯ y = 41.45, variance s 2 y = 5.23, from population B. Please calculate the degree of freedom in order to use the general procedure. 9 24 36 25 21 3 points Save Answer QUESTION 20 Based on previous problem, p lease set up the 99% con±dence interval for di²erence of the population means. (-14.04, -3.96) 3 points Save Answer Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.

(-13.55, -4.12) (-12.06, -6.82) (-11.35, -5.81) (-10.90, -7.10) Remaining Time: 1 hour, 09 minutes, 56 seconds. Click Save and Submit to save and submit. Click Save All Answers to save all answers.