Page 1 of 4 Exam #1 (This is just an example!) 1. True/False Questions: circle the right answer. 1) A bar chart is an example of a numerical measure. True / False 2) Primary data are the data that are collected by the project manager himself. True / False 3) In statistical terms, a population is defined as a collection of people that live in a particular region of the country. True / False 4) If a state agency wishes to conduct on-site surveys of small businesses throughout the state, cluster sampling could potentially be used to reduce the geographical area over which the surveys would need to be conducted. True / False 2. Multiple Choices: only one of the answer is correct. 1) If a systematic random sample is to be selected of size 100 from a population with 5,000 items, the first item selected from the ordered population will be -- ( B ) A) randomly selected between 1 and 100. B) randomly selected between 1 and 50. C) any randomly selected value between 1 and 5,000. D) item 50. -- With systematic sampling, you first decide the interval= 5000/100 = 50. Hence the first one is going to be from 1 to 50. the next one is the first one + 50, … 2) The human resources department at a major high tech company recently conducted an employee satisfaction survey of 100 of its 3000 employees. Data were collected on such variables as age, gender, marital status, current salary, level of overall satisfaction on a scale from 1 to 5, number of years with the company, and job title. Which of the variables listed are considered to be RATIO level data? --- ( A )Bus 304 Exam #1 (Sample) Page 2 of 4 A) Age and years with the company B) Gender and marital status C) Job title D) None of the variables is ratio level. Both age and years are numbers allowing some level of mathematical analysis Æ interval or ratio. They are particularly ratio because -- A person with age 0 is an unborn child (non-existing, no such person yet). -- A person having 0 year with the company is the one who has no experience with the company yet. 3) If two variables show a positive linear relationship in a scatter diagram: --( B ) A) most of the data values will plot in the lower left-hand quadrant. B) most of the data values will plot in the lower left-hand and upper right-hand quadrants. C) most of the data values will cluster close to the x and y axes. D) None of the above. -- for example. 4) Consider the following sample data: 25 11 6 4 2 17 9 6 which of the following histogram correctly represents the sample distribution?–( D ) A) 4210100.511.522.533.544.51~6 7~12 13~18 19~24 25 andmo re B) 2320100.511.522.533.51~5 6~10 11~15 15~20 20~25 C)2311100.511.522.533.51~5 6~10 11~15 15~20 20~25 D) Both A and C All of them. You can verify this by simply counting on how many values fall in each range. This exercise reminds you that a histogram is a subject graph, depending on how you group your data (choosing the number of groups, boundaries), the result may look different. That’s one of the reasons why computer can not automatically generate one for you.Bus 304 Exam #1 (Sample) Page 3 of 4 5) Assume that students’ score follow a normal distribution with mean 80 and standard deviation 10. What is the probability that a student’s score is higher than 90? – ( C ) A) 0 B) 0.1 C) 0.1587 D) 0.3413 Z90 = 1 Î Table reports that P(80<x<90) = 0.3413 Î P (x>90) = 0.5 – 0.3413 = 0.1587 3. Below is a probability distribution chart. x in the graph represents the number of cars sold a day in a car dealership. (Note, the data were not real. DO NOT use it outside the classroom.) Answer the following questions: (1) (3 points) What is the probability that less than 2 cars are sold? P (x < 2) = P (x=0) + P (x=1) = 0.1 + 0.25 = 0.35 (2) (4 points) What is the expected number of cars sold a day? (3) (6 points) What is the variance? x P(x) x*P(x) x-E(x) (x-E(x))2 (x-E(x))2*P(x) 0 0.1 0 -1.95 3.8025 0.380251 0.25 0.25 -0.95 0.9025 0.2256252 0.35 0.7 0.05 0.0025 0.0008753 0.2 0.6 1.05 1.1025 0.22054 0.1 0.4 2.05 4.2025 0.42025SumÆ 1.00 (verify) E(x)=1.95 Var (x) = 1.2475(4) (3 points) What is the standard deviation? Sd (x) = sqrt(1.2475) = 1.116915 ~1.12 80 90 xf(x) 0.3413 0.5 – 0.3413 = 0.1587 Probability Distribution00.050.10.150.20.250.30.350.401234XP(X)Bus 304 Exam #1 (Sample) Page 4 of 4 4. The following data contain a sample of 50 households’ annual income. Below is a low-tech solution of creating a histogram. You can also input the numbers in computer and use excel to help you finish this problem. Your choice. $55,834.75 $49,643.52 $69,446.39 $50,814.03 $62,291.44$78,663.86 $37,296.34 $95,139.62 $83,084.23 $52,176.44$94,147.10 $60,335.56 $73,720.73 $88,532.87 $69,556.84$92,975.25 $63,397.39 $72,207.64 $103,783.73 $74,512.81$100,997.00 $43,231.03 $67,301.89 $73,732.24 $75,421.76$42,246.19 $66,481.13 $104,583.18 $67,143.07 $70,159.26$71,487.28 $68,939.29 $87,985.09 $35,127.08 $47,917.52$41,425.34 $77,022.80 $110,634.82 $69,280.14 $48,862.76$58,699.49 $69,517.61 $65,176.40 $86,364.17 $63,952.85$34,646.94 $70,095.14 $99,921.84 $53,337.20 $36,336.29Create a histogram with 5 classes to present the income distribution. The bin values are suggested below. $20,000<x<$39,999 $40,000<x<$59,999 $60,000<x<$79,999 $80,000<x<$99,999 $100,000<x<$119,999 5. Normal probability distribution If µ=20, and σ2=16, compute the following probabilities: σ=4 (a) (4points) P( 25)x > (b) (4 points) P( 18)x < (c) (4 points) P(18