Practice Test 1 Business Statistics:Multiple Choice: Each is worth two pointsIdentify the letter of the choice that best completes the statement or answers the question. **Skip 15-17,18,20 Ch10-12,13 Material____ 1. The sum of the relative frequencies for all classes will always equal a.the sample sizeb.the number of classesc.oned.any value larger than one____ 2. The interquartile range isa.the 50th percentileb.another name for the variancec . the difference between the largest and smallest valuesd . the difference between the third quartile and the first quartile____ 3. The standard deviation of a sample of 100 observations equals 64. The variance of the sample equalsa.8b.10c.6400d.4,096____ 4. The numerical value of the standard deviation can never bea.larger than the variance.cnegative.smaller than the varianced.____ 5. The set of all possible sample points (experimental outcomes) is called aa sample.an eventb.cthe sample space.a populationd.____ 6. A random variable that can assume only a finite number of values is referred to as a(n)infinite sequencea.bfinite sequence.discrete random variablec.discrete probability functiond.Exhibit 5-11A local bottling company has determined the number of machine breakdowns permonth and their respective probabilities as shown below:Number ofBreakdowns Probability0 0.121 0.382 0.253 0.184 0.07____ 7. Refer to Exhibit 5-11. The probability of at least 3 breakdowns in a month is a0.5b0.10.c0.30.d0.90.____ 8. A normal probability distributionis a continuous probability distributiona.bis a discrete probability distribution.can be either continuous or discretec.dmust have a standard deviation of 1.Exhibit 6-6The starting salaries of individuals with an MBA degree are normally distributedwith a mean of $40,000 and a standard deviation of $5,000.____ 9. Refer to Exhibit 6-6. What percentage of MBA's will have starting salaries of $34,000 to $46,000?a38.49%.38.59%b.50%c.76.98%d.____10. Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901?1.96a.-1.96b.0.4505c.d 1.65____11. Which of the following is not a measure of central location?amean.medianb.variancec.moded.____12. The descriptive measure of dispersion that is based on the concept of a deviation about the mean isthe rangea.the interquartile rangeb.the absolute value of the rangec.the standard deviationd.____13. Which of the following symbols represents the mean of the population?aσ2.bσ.cμ.d.____14. Which of the following symbols represents the size of the sampleaσ2.bσ.Nc.d n____15. If two events are independent, thenathey must be mutually exclusive.the sum of their probabilities must be equal to oneb.ctheir intersection must be zero.None of these alternatives is correct..d.____16. Which of the following statements is(are) always true?a-1 ≤ P(E i) ≤1.P(A) = 1 - P(A c)b.P(A) + P(B) = 1c.d∑P ≥ 1.____17. A measure of the average value of a random variable is called a(n)variancea.bstandard deviation.expected valuec.coefficient of variationd.____18. Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly twocustomers in the sample will default on their payments?0.2592a.0.0142b..0.7408d.____19. The expected value of a discrete random variablea. is the most likely or highest probability value for the randomvariableb. will always be one of the values x can take on, although it maynot be the highest probability value for the random variablec. is the average value for the random variable over many repeats ofthe experimentd. None of these alternatives is correct.____20. Which of the following is not a property of a binomial experiment?a. the experiment consists of a sequence of n identical trialsb. each outcome can be referred to as a success or a failurec. the probabilities of the two outcomes can change from onetrial to the nextd. the trials are independentExhibit 5-9The probability distribution for the daily sales at Michael's Co. is given below.Daily Sales(In $1,000s) Probability40 0.150 0.460 0.370 0.2____21. Refer to Exhibit 5-9. The expected daily sales are$55,000a.$56,000b.$50,000c.$70,000d.azero.-0.5b.c0.5.oned.Exhibit 6-2The weight of football players is normally distributed with a mean of 200 poundsand a standard deviation of 25 pounds.____23. Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds?a. 28.81%b0.5762%.c. 0.281%57.62%d.Exhibit 6-6The starting salaries of individuals with an MBA degree are normally distributedwith a mean of $40,000 and a standard deviation of $5,000.____24. Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500?a. 0.4332b. 0.9332c. 0.0668d. 0.5000Short Answer/Problems1.The following data represent the daily demand (y in thousands of units) and the unit price (xin dollars) for a product.Daily Demand (y) Unit Price (x)47 139 335 544 334 620 815 16a. Compute and interpret the sample covariance for the above data.b. Compute and interpret the sample correlation coefficient.2.The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and astandard deviation of $6.a. What is the probability that a randomly selected bill will be at least $39.10?b. What percentage of the bills will be less than $16.90?c. What are the minimum and maximum of the middle 95% of the bills?d. If twelve of one day's bills had a value of at least $43.06, how many bills didthe restaurant collect on that day?3.Below you are given a partial computer output based on a sample of 7 observations, relatingan independent variable (x) and a dependent variable (y).Predictor Coefficient StandardErrorConstant 24.112 8.376x -0.252 0.253Analysis of VarianceSOURCE SSRegression 196.893Error 94.822a. Develop the estimated regression line.b. If you are given that x = 50, find the estimate of y based on your regressionequation.c. Determine the coefficient of determination and interpret your answer. Solutions to MC1. C2. D3. D4. C5. C6. C7. D8. A9. D 10. D11. C 12. D 13. C 14. D 15. D 16. B 17. C 18. B19. C 20. C 21. B 22. C 23. D 24. C 25. C 26. A27. B 28. D 29. CSolutions to Short Answer1. ANS:a. -47 (rounded). Since the covariance is negative, it indicates a negativerelationship between x and y.b. -0.922. There is a strong negative relationship between x and y.2. ANS:a. 0.0322b. 0.0322d. 2,0003. ANS:a. = 24.112 + 0.816xb. If x = 50 then = 24.112 + 0.816x 24.1 + 0.82 ( 50 ) = 65.1c. 0.675 So there is a fairly strong positive relationship between x and y.Practice Test 2 Business Statistics:Multiple Choice: Each is worth two pointsIdentify the letter of the choice that best completes the statement or answers the question.____ 1. The sample statistic s is the point estimator ofa. μbσ.c.d.____ 2. A sample statistic is an unbiased estimator of the population parameter ifa. the expected value of the sample statistic is equal to zerob. the expected value of the sample statistic is equal to onec. the expected value of the sample statistic is equal to thepopulation parameterd. it is equal to zero____ 3. A property of a point estimator that occurs whenever larger sample sizes tend to provide point estimates closer to the population parameter is known asa. efficiencyb. unbiased samplingc. consistencyd. relative estimation____ 4. A random sample of 121 bottles of cologne showed an average content of 4 ounces.It is known that the standard deviation of the contents (i.e., of the population) is 0.22ounces. In this problem the 0.22 isa. a parameterb. a statisticd. the average content of colognes in the long run____ 5. A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximatelya. normal because is always approximately normally distributedb. normal because the sample size is small in comparison to thepopulation sizec. normal because of the central limit theoremd. None of these alternatives is correct.____ 6. As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distributiona. becomes largerb. becomes smallerc. stays the samed. None of these alternatives is correct.____ 7. From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. Thestandard error of the mean isa. 3b. 2c. greater than 2d. less than 2____ 8. Which of the following is(are) point estimator(s)?a. σb. μc. sd. α____ 9. A population characteristic, such as a population mean, is calleda. a statistica parameterb.c. a sampledthe mean deviation.____10. The sample statistic, such as , s, or , that provides the point estimate of the population parameter is known asa. a point estimatorb. a parameterc. a population parameterd. a population statistic____11. The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on thea. central limit theoremb. fact that we have tables of areas for the normal distributionc. assumption that the population has a normal distributiond. None of these alternatives is correct.____12. Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation ofthe sampling distribution of the sample means area. 8.7 and 1.94b. 36 and 1.94c. 36 and 1.86d. 36 and 8____13. When constructing a confidence interval for the population mean and a small sample is used, the degrees of freedom for the t distribution equalsa. n-1b. nc. 29d. 30_____ 14. The collection of all possible sample points in an experiment isa. the sample spaceb. a sample pointc.an experimentd. the population_____ 15. Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?a. 20b. 7c. 5!d. 10_____ 16. The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many “Top Three”outcomes are there?a. 302,400b. 720c. 1,814,400d. 10_____ 17. Given that event E has a probability of 0.25, the probability of the complement of event Ea. cannot be determined with the above informationb. can have any value between zero and onec. must be 0.75d. is 0.25_____ 18. The symbol ⋃ shows thea.union of eventsb. intersection of eventsc.sum of the probabilities of eventsd.sample space_____ 19. If P(A) = 0.38, P(B) = 0.83, and P(A ⋂ B) = 0.57; then P(A ⋃ B) =a. 1.21b. 0.64c. 0.78d. 1.78_____ 20. If P(A) = 0.62, P(B) = 0.47, and P(A ⋃ B) = 0.88; then P(A ⋂ B) =a. 0.2914b. 1.9700c. 0.6700d.0.2100_____ 21. If P(A) = 0.85, P(A ⋃ B) = 0.72, and P(A ⋂ B) = 0.66, then P(B) =a. 0.15b. 0.53c. 0.28d. 0.15_____ 22. Two events are mutually exclusive ifa. the probability of their intersection is 1b. they have no sample points in commonc. the probability of their intersection is 0.5d. the probability of their intersection is 1 and they have no sample points in common_____ 23. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ⋂ B) =a. 0.30b. 0.15c. 0.00d. 0.20_____ 24. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ⋃ B) =a. 0.00b. 0.15c. 0.8d. 0.2_____ 25. A subset of a population selected to represent the population is aa.subsetb.samplec.small populationd. None of the alternative answers is correct._____ 26. A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should havea. the same probability of being selectedb. a probability of 1/n of being selectedc. a probability of 1/N of being selectedd. a probability of N/n of being selected_____ 27. A probability distribution for all possible values of a sample statistic is known as aa.sample statisticb.parameterc.simple random sampled.sampling distribution_____ 28. From a population of 200 elements, the standard deviation is known to be 14.A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean isa. 3b. 2c. greater than 2d. less than 2_____ 29. From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximatelya. 1.1022b. 2c. 30d. 1.4847Short Answer/ProblemsDirections: Clearly designate your solution to each portion of the questions asked and show your entire work and method for arriving at the solution.1. The sales records of a real estate agency show the following sales over the past 200 days:b. Assign probabilities to the sample points and show their values.c. What is the probability that the agency will not sell any houses in a given day?d. What is the probability of selling at least 2 houses?e. What is the probability of selling 1 or 2 houses?f. What is the probability of selling less than 3 houses?2. Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and P(B)= 0.4.a. Find P(A ⋂ B).b. Find P(A ⋃ B).c. Find P(A⎜B).3.You are given the following information on Events A, B, C, and D. P(A) = .4, P(B) = .2,P(C) = .1,P(A ⋃ D) = .6, P(A⎜B) = .3, P(A ⋂ C) = .04, P(A ⋂ D) = .03a. Compute P(D).b. Compute P(A ⋂ B).c. Compute P(A⎜C).d. Compute the probability of the complement of C.e. Are A and B mutually exclusive? Explain your answer.f. Are A and B independent? Explain your answer.g. Are A and C mutually exclusive? Explain your answer.h. Are A and C independent? Explain your answer.4. Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and 9 ounces.a. Determine the mean and the variance of the population.b. Sampling without replacement from the above population with a sample sizeof 2 produces ten possible samples. Using the ten sample mean values, determinethe mean of the population and the variance of .c. Compute the standard error of the mean.5. A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.a. What are the expected value, standard deviation, and shape of the samplingdistribution of the sample mean?b. What is the probability that these 64 students will spend a combined total of morethan $715.21?c. What is the probability that these 64 students will spend a combined total between$703.59 and $728.45?Solutions to MC Problems1. B 2 C 3. C 4. A 5. C 6. B 7. D 8. C 9. B 10. A11. A 12. C 13. A 14. A 15. D 16. B 17. C 18. A19. B 20. D 21. B 22. B 23. C 24. C 25. B 26. A27. D 28. D 29. DShort Answer/ProblemsDirections: Clearly designate your solution to each portion of the questions asked and show your entire work and method for arriving at the solution.1. ANSWERS:2. ANSWERS:a. 0.0 b. 0.6 c. 0.03ANSWERS:a. 0.23b. 0.06c. 0.4d. 0.9e. No, P(A⎜B) ≠ 0f. No, P(A⎜B) ≠ P(A)g. No, P(A ⋂ C) ≠ 0h. Yes, P(A⎜C) = P(A)4. ANSWERS:a. 5 and 8b. 5 and 3c. 1.7325. ANSWERS:a. 10.5 0.363 normalb. 0.0314c. 0.0794。