BU255 Practice Questions

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Wilfrid Laurier University *

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255

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Statistics

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Jan 9, 2024

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WEEK ONE 1.7 Classify each of the following as nominal, ordinal, interval, or ratio data. a. The time required to produce each tire on an assembly line RATIO b. The number of liters of milk a family drinks in a month RATIO c. The ranking of four machines in your plant after they have been designated as excellent, good, satisfactory, and poor ORDINAL d. The telephone area code of clients in Canada NOMINAL e. The age of each of your employee RATIO f. The dollar sales at the local pizza house each month RATIO g. An employee’s identification number NOMINAL h. The response time of an emergency unit RATIO 1.8 Classify each of the following as nominal, ordinal, interval, or ratio data. a. The ranking of a company by Report on Business magazine’s Top 1000 ORDINAL b. The number of tickets sold at a movie theatre on any given night RATIO c. The identification number on a questionnaire NOMINAL d. Per capita income RATIO e. The trade balance in dollars RATIO f. Profit/loss in dollars RATIO g. A company’s tax identification number NOMINAL h. The Standard & Poor’s bond ratings of cities based on the following scales: ORDINAL 1.9 There is a Video associated with this question. The Mapletech Manufacturing Company makes electric wiring, which it sells to contractors in the construction industry. Approximately 900 electrical contractors purchase wire from Mapletech annually. Mapletech’s director of marketing wants to determine electrical contractors’ satisfaction with Mapletech’s wire. She develops a questionnaire that yields a satisfaction score of between 10 and 50 for participant responses. A random sample of 35 of the 900 contractors is asked to complete a satisfaction survey. The satisfaction scores for the 35 participants are averaged to produce a mean satisfaction score. a. What is the population for this study? 900 ELECTRICAL WORKERS b. What is the sample for this study? THE 35 SELECTED c. What is the statistic for this study? THE STATISTIC IS THE AVERAGE SCORE FOR THE SAMPLE d. What would be a parameter for this study? THE PARAMETER IS THE AVERAGE SCORE FOR THE POPULATION 2.25 There is a Video associated with this question. For the following data, construct a frequency distribution with six classes.

CLASS INTERVAL FREQUENCY 10 - 20 3 20 - 30 12 30 - 40 5 40 - 50 6 50 - 60 4 2.26 For each class interval of the frequency distribution given, determine the class midpoint, the relative frequency, and the cumulative frequency. CLASS FREQUENCY MIDPOINT REL. FREQ CUM. FREQ 20 - under 25 17 22.5 .207 17 25 - under 30 20 27.5 .244 37 30 - under 35 16 32.5 .195 53 35 - under 40 15 37.5 .183 68 40 - under 45 8 42.5 .098 76 45 - under 50 6 47.5 .073 82 3.11 A data set contains the following seven values. 6 2 4 9 1 3 5 a. Find the range. b. Find the mean absolute deviation. c. Find the population variance. d. Find the population standard deviation. e. Find the interquartile range. f. Find the z score for each value.

4.2 Given X = {1, 3, 5, 7, 8, 9}, Y = {2, 4, 7, 9}, and Z = {1, 2, 3, 4, 7}, solve the following. a. X ∪ Z = (1,2,3,4,5,7,8,9) b. X ∩ Y = (7,9) c. X ∩ Z = (1,3,7) d. X ∪ Y ∪ Z = (1,2,3,4,5,7,8,9) e. X ∩ Y ∩ Z = (7) f. (X ∪ Y) ∩ Z = (1,2,3,4,7) g. (Y ∩ Z) ∪ (X ∩ Y) = (2,4,7,9) h. X or Y = (1,2,3,4,5,7,8,9) i. Y and Z = (2,4,7) 4.3 If a population consists of the positive even numbers through 30 and if A = {2, 6, 12, 24}, what is Aʹ? A’ = 4,8,10,14,16,18,20,22,26,28,30 4.10 Use the values in the matrix to solve the equations given E F A 0.10 0.03 0.13 B 0.04 0.12 0.16 C 0.27 0.06 0.33 D 0.31 0.07 0.38 0.72 0.28 a. P(A ∪ F) = P(A) + P(F) - P(A∩F) = ( 0.13 + 0.28) - 0.03 = 0.38 b. P(E ∪ B) = P(E) + P(B) - P(E∩B) = (0.72 + 0.16) - 0.04 = 0.84 c. P(B ∪ C) = P(B) + P(C) = 0.16 + 0.33 = 0.49 d. P(E ∪ F) = P(E) + P (F) = 0.72 + 0.28 = 1.00 4.13 A survey estimated that 67% of all households with television subscribe to a digital streaming service. Seventy-four percent of all households with television have two or more TV sets. Suppose 55% of all households with television subscribe to a digital streaming service and have two or more TV sets. A household with television is randomly selected. P(A) = 0.67,,,, P(B) = 0.74,,,,, P(A∩B) = 0.55,,,,, a. What is the probability that the household subscribes to a streaming service or has two or more TV sets? P(A ∪ B) = P(A) + P(B) - P(A∩B) = (0.67 + 0.74) - 0.55 = 0.86 b. What is the probability that the household subscribes to a streaming service or has two or more TV sets but not both?

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P(A ∪ B but not both) = P(A ∪ B) - P(A∩B) = 0.86 - 0.55 = 0.31 c. What is the probability that the household neither subscribes to a streaming service nor has two or more TV sets? P(NONE) = 1 - P(A ∪ B) = 1 - 0.86 = 0.14 d. Why does the special law of addition not apply to this problem? The special law of addition does not apply because P(A∩B) doesn’t = 0.000. The following two events are not mutually exclusive 4.16 Use the values in the probability matrix to solve the equations given. a. P(E ∩ B) = 0.09 b. P(C ∩ F) = 0.06 c. P(E ∩ D) = 0.00 4.19 According to the Canadian Tourism Human Resource Council, 11% of all Canadians in the labour force are employed in the tourism industry. Fifty-one percent of those who work in this sector are under 35 years of age. Assume that of those in the Canadian labour force not employed in the tourism industry, only 44% are under 35. Suppose you choose someone randomly from the Canadian labour force. Let T = employed by tourism,,,,, Let U = under 35,,,,, P(T)=0.11,,,,, P(U|T)=0.51,,,,, P(U|NT)=0.44 a. What is the probability that this person is not employed by the tourism industry? P(NT)= 1 - P(T) = 1 - 0.11 = 0.89 b. What is the probability that this person is employed by the tourism industry and is under 35 years of age? P(T∩U) = P(U|T)*P(T) = 0.51*0.11 = 0.056 c. What is the probability that this person is employed by the tourism industry and is over 35 years of age? P(T∩NU) = P(T)* P(NU|T) = 0.11*(1-0.51) = 0.054 d. What is the probability that this person is not employed by the tourism industry and is under 35 years of age? P(NT∩U) = P(U|NT)*P(NT) = 0.44*0.89 = 0.392 e. What is the probability that this person is not employed by the tourism industry and is over 35 years of age?

P(NT∩NU) = P(NT)*(1-P(U|NT)) = 0.89*0.56 = 0.498 f. What is the probability that this person is neither employed by the tourism industry nor over 35 years of age? P(NT∩U) = P(NT)*P(U|NT) = 0.89*0.44 = 0.391 g. What is the probability that this person is neither employed by the tourism industry nor under 35 years of age? P(NT∩U) = P(NT)*P(NU|NT) = 0.89*(1-0.44) = 0.498 4.24 Use the values in the probability matrix to solve the equations given. a. P(C|A) = P(C∩A)/P(A) = 0.36/0.8 = 0.45 b. P(B|D) = P(B∩D)/P(D) = .169 c. P(A|B) = .00 4.27 A survey of U.S. small-business owners was conducted to determine the challenges for growth for their businesses. The top challenge, selected by 46% of the small-business owners, was the economy. A close second was finding qualified workers (37%). Suppose 15% of the small-business owners selected both the economy and finding qualified workers as challenges for growth. A small-business owner is randomly selected. P(E) = 0.46%,,,,,,,P(Q) = 0.37%,,,,,,, P(E∩Q) = 0.15% a. What is the probability that the owner believes the economy is a challenge for growth if the owner believes that finding qualified workers is a challenge for growth? P(E|Q) = P(E∩Q)/P(Q) = 0.15/0.37 = 0.405 b. What is the probability that the owner believes that finding qualified workers is a challenge for growth if the owner believes that the economy is a challenge for growth? P(Q|E) = P(Q∩E)/P(E) = 0.15/0.46 = 0.326 c. Given that the owner does not select the economy as a challenge for growth, what is the probability that the owner believes that finding qualified workers is a challenge for growth? P(NE|Q) = P(NE∩Q)/P(Q) = ((1 - E)∩Q)/ d. What is the probability that the owner believes neither that the economy is a challenge for growth nor that finding qualified workers is a challenge for growth?

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