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KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DEPARTMENT OF MATHEMATICAL SCIENCES DHAHRAN, SAUDI ARABIA STAT 211: BUSINESS STATISTICS I Semester 062 Mid Term Exam No.1 Wednesday March 28, 2007 5:30 – 7:15 pm Please circle your: Instructor’s name & section number Prof. Hassen A .Muttlak 1 Mohammad F. Saleh 2 3 4 Name: Student ID#: Serial #: Directions: 1) You must show all work to obtain full credit for questions on this exam. 2) DO NOT round your answers at each step. Round answers only if necessary at your final step to 4 decimal places. Question No Full Marks Marks Obtained Part One 8 Part Two 8 Q1 12 Q2 5 Q3 5 Q4 10 Q5 22 Total 70 STAT 211 Business Statistics I – Term 062, Major 1 Part One (8 pts, 1 for each) Indicate which of the following TRUE or FALSE 1. The classes in any frequency distribution are both all inclusive and mutually exclusive._______ 2. A tire store manager has collected data showing the number of tires of each brand sold during the past month. A bar chart might be effective in graphically illustrating which brands tend to sell best at this store. _______ 3. One of the most effective methods for displaying the trend in the number of traffic accidents over the past ten years is to use a scatter plot showing the number of vehicles on one axis and the number of accidents on the second axis. _______ 4. Telephone surveys are most frequently used for political polls. The reason is that the survey can be conducted in a shorter time span (usually over a 24 hour period.) _______ 5. When students are asked to list their age and the percentage of their college expenses that they pay for themselves, the type of data being collected is quantitative. _______ 6. When a group of university students take a poll of their fellow students on whether they support a proposed fee increase, the sampling method they would use when students walking near the library are surveyed would be called a random sample. _______ 7. If you wish to select a non statistical sample of opinions from customers at a particular market, the method that you might consider using is cluster sampling. ______ 8. A small engine repair shop tracks the number of customers who call each day. This variable is a time series variable and also ratio level._______ 2 STAT 211 Business Statistics I – Term 062, Major 1 Part Two (8 pts 1 for each) Circle the correct answer: 1. Which of the following statements about histogram is correct? a. The rectangles (bars) are proportional in height to the number of items falling in the classes b. There are generally five rectangles (bars) in each histogram c. The area in a rectangle (bar) depends only on the number of items in the class compared to the number of items in all other classes. d. Narrow class intervals can obscure important patterns of variation. 2. The Fitness Center manager has collected data on the number of visits to the club each week for the past 8 weeks. These data are shown as follows. Which of the following statements is most correct? Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 1415 1623 1934 1879 2102 2156 2511 2499 a. A histogram will illustrate whether a linear relationship exists between the number of visits and the week number. b. A scatter diagram would be useful for displaying these data. c. A line chart for these data will show that an upward trend in the number of visits to the club has occurred over the past 8 weeks. d. The proper graph for displaying these data is a pie chart. 3. A scatter diagram can be used to do which of the following? a. Determine the trend in a variable b. Analyze the relationship between two variables c. Describe the basic distribution for a quantitative variable d. Show the percentage of a variable that is associated with each category into which that variable has been divided. 4. The mode has all the following disadvantages except a. A data set may have no model value. b. Every value in a data set may be a mode. c. The mode may not reflect the center of a data. d. The mode is not effected by the extreme values 3 STAT 211 Business Statistics I – Term 062, Major 1 5. Which of the following statements in NOT correct? a. Calculation of a mean is affected by the extreme values. b. The median is the preferred measure of central location for ordinal data instead of the mean. c. The mean can be found for all levels of data measurements. d. The sum of the differences between each observation in a data set and the mean of the data set always zero. 6. A tire manufacturing company is interested in obtaining data on stopping distances for each of the three main tread types made by the company. The data collection method that would be most likely used in this case would be: a. Telephone survey. b. Written questionnaire. c. Demographic surveying. d. Experiments. 7. Under what circumstances is it necessary to use the coefficient of variation to compare relative variability between two or more distributions a. When the means of the distributions are equal b. When the means of the distributions are not equal c. When the standard deviations of the distributions are not equal d. When the standard deviations of the distributions are equal 8. The human resources department at a major high tech company recently conducted an employee satisfaction survey of 100 of its 3,000 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 would be considered to be qualitative data? a. Gender, marital status, job satisfaction, and job title b. Age c. Years with the company d. All variables listed are qualitative. 4 STAT 211 Business Statistics I – Term 062, Major 1 Part Three Question One (6+3+3 pts): A computer company compiled data regarding the number of interviews required for each of its 40 salespeople to make a sale. Following are a frequency distribution and a relative frequency distribution of the number of interviews required per salesperson per sale. a. Fill the missing data Number of interviews Frequency Relative frequency 0.200 10 0.150 [40 – 50) 0.025 Total b. Construct a frequency histogram. c. Explain what information can be conveyed by a frequency histogram. 5 STAT 211 Business Statistics I – Term 062, Major 1 Question Two (5 pts): A set of 60 observations has a mean of 66.8 and a standard deviation of 3.55, if the distribution is symmetric and has bell shape, approximately how many observations should be found in the interval 59.7 and 73.9? Question Three (5 pts): Incomes in a particular market area are known to be right-skewed with a mean equal to $33,100. In a report issued recently, a manager stated that at least 88 percent of all incomes are in the range of $26,700 to $39,500, what is the standard deviation for the incomes in this market area? 6 STAT 211 Business Statistics I – Term 062, Major 1 Question Four (5+5 pts): Bassart Electronics is considering employing one of two training programs. Two groups were trained for the same task. Group 1 was trained by program A; group 2, by program B. for the first group, the times required to train the employees had the average 32.11 hours and variance 68.09. In the second group, the average was 28.75 hours and the variance was 123.21. a. Which training program has less relative variability in its performance? Explain. b. If two employees, one from each group, needed 50 training hours, which employee is closer to an average employee in his group? Explain. 7 STAT 211 Business Statistics I – Term 062, Major 1 Question Five (5+2+6+9 pts): Farm stores compares prices charged for identical items in all of its food stores. Here are the prices (in SR) charged by each store for a kg of meat 31.4 28.5 31.7 36.0 38.6 33.1 45.0 31.4 35.4 30.5 Given that xi 341.6 and xi 2 11879.04 a. Calculate the sample mean price per kg and the sample median price per kg. b. Which value is better measure of the central tendency of these data? Explain c. Calculate the sample standard deviation and the coefficient of variation and comment of the variation of the data. 8 STAT 211 Business Statistics I – Term 062, Major 1 d. Construct a box and whisker plot, and comment on the shape. 9