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KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
DEPARTMENT OF MATHEMATICAL SCIENCES
DHAHRAN, SAUDI ARABIA
STAT 211: BUSINESS STATISTICS
Final Exam, Semester-051 (2005)
Time: 12:30 pm to 3:00 pm. Monday, January 30, 2006.
Instructors: Musawar Amin Malik, Mohammad H. Omar
Student Name: ID# Section #
Answer all questions. And show all work. You are allowed to use any electronic calculator.
|Question No | Marks |Marks Obtained |
| | | |
|1 to 19 |19 | |
|20 to 28 |9 | |
|29 |10 | |
|30 |10 | |
|31 |10 | |
|32 |10 | |
|33 |15 | |
|34 |12 | |
|35 |5 | |
|Total |100 | |
| | | |
Part I. (19 marks).
Answer the following questions by marking True or False.
1. A class project calls for the students to access the data compiled from 2000 U.S. Census. The data that the students would be using are considered primary data by the students.
2. The Georgia Company, a pharmaceutical company, recently conducted a study in which 20 people were given a new drug and 20 other people were given a placebo. The objective was to determine whether there was a difference in pain relief between those using the new drug versus those using the placebo. The data collection used here is an example of an experiment.
3. If you plan to collect data using an experiment, you will typically be interested in establishing specific controls on certain variables that might impact the results of the experiment.
4. 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.
5. If stratified random sampling is performed correctly, one of the advantages is that the total required sample size to generate a specified level of information may be less than what would be required from a simple random sample.
6. A variable representing the length of time it takes for an employee to complete an assembly procedure at an automotive plant, is a ratio level variable.
7. When developing a frequency distribution for continuous data, typically the variable of interest needs to be organized into mutually exclusive classes.
8. It is often a good idea to convert frequency distributions to relative frequency distributions when you wish to compare two distributions with different amounts of data.
9. A study was recently conducted in which makers of toothpaste tracked sales for the month at different stores in a market area. The variable of interest was the number of units sold. The numbers ranged from 1,200 to 22,700. In this case, the stems in a stem & leaf diagram might be values such as 1 and 22 while the leaves would be 200 and 700.
10. A scatter diagram is a line graph without the points connected by a line.
11. You are given the following data:
23 34 11 40 25 47
Assuming that these data are a sample selected from a larger population, the median value for these sample data is 25.5.
12. The Good-Guys Car Dealership has tracked the number of used cars sold at its downtown dealership. Consider the following data as representing the population of cars sold in each of the 8 weeks that the dealership has been open.
3 5 2 7 7 7 9 0
The population range is 3.
13. The distribution of bankcard balances for customers is highly right-skewed with a mean of $1,100 and a standard deviation equal to $250. Based on this information, approximately 68 percent of the customers will have bank balances between $850 and $1,350.
14. The weight of a box of nails at a hardware store is an example of a discrete random variable since there are only a certain number of nails in the box.
15. If the value of one discrete random variable increases, while the value of a second discrete random variable tends to decrease, these two variables are said to be uncorrelated.
16. The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request non-smoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting non-smoking rooms is described by a binomial distribution, the expected number of requests for non-smoking rooms is 14.
17. The product manager for a large retail store has recently stated that she estimates that the average purchase per visit for the store’s customers is between $33.00 and $65.00. The $33.00 and the $65.00 are considered point estimates for the true population mean.
18. The makers of Crustfree Bread in Boston have a quality standard that calls for an average of 3 burned loaves per batch. Assuming that the average of three per batch is being met, the standard deviation for the number of burned loaves in 4 batches is approximately 1.73 loaves.
19. An electronics repair shop has determined that the time between failures for a particular electronic component part is exponentially distributed with a mean time between failures of 200 hours. Based on this information, the probability that a part will fail in the first 20 hours is approximately 0.095.
Part II. (9 marks).
Answer the following questions by circling the best answer.
20. 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.
21. Another term used for statistical sampling is:
a. probability sampling.
b. convenience sampling.
c. ratio sampling.
d. numerical sampling.
22. 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. Age and years with the company
b. Gender and marital status
c. Job title
d. None of the variables is ratio level.
23. Which of the following is a key difference between a bar chart and a histogram?
a. A bar chart typically has gaps between the bars while a histogram has no gaps.
b. A bar chart is developed to analyze a continuous variable, while a histogram is used to analyze discrete variables.
c. Both a and b are correct.
d. There is actually no real difference between a bar chart and a histogram.
24. Consider the following chart. Which of the following statements is most correct?
a. There is a negative linear relationship between the two variables.
b. There is a positive linear relationship between the two variables.
c. There is a perfect linear relationship between the two variables.
d. There is no apparent relationship between the two variables.
25. A large retail company gives an employment screening test to all prospective employees. Frankin Gilman recently took the test and it was reported back to him that his score placed him at the 80th percentile. Therefore:
a. 80 people who took the test scored below Franklin.
b. Frankin scored as high or higher than 80 percent of the people who took the test.
c. Frankin was in the bottom 20 percent of those that have taken the test.
d. Frankin’s score has a z-score of 80.
26. In order to compute the mean and standard deviation, the level of data measurement should be:
a. ratio or interval.
27. The following probability distribution has been assessed for the number of accidents that occur in a mid-western city each day:
Based on this distribution, the expected number of accidents in a given day is:
d. None of the above.
28. Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $0.35 and a standard deviation of $0.33. Based on this information, what is the probability that a randomly selected stock will be at most $0.40?
Part III. (72 marks).
29. The monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00. If a statistical sample of n = 100 customers is selected at random, what is the probability that the mean bill for those sampled will not exceed $75.00?
30. A claim was recently made on national television that two of every three doctors recommend a particular pain killer. Suppose a random sample of n = 300 doctors revealed that 180 said that they would recommend the painkiller. If the TV claim is correct, what is the probability of 180 or fewer in the sample agreeing?
31. One of the major oil products companies conducted a study recently to estimate the mean gallons of gasoline purchased by customers per visit to a gasoline station. To do this, a random sample of customers was selected with the following data being recorded that show the gallons of gasoline purchased.
Based on these sample data, construct and interpret a 95 percent confidence
interval estimate for the population mean.
32. A financial analyst is interested in estimating the proportion of publicly traded companies on the New York Stock Exchange that have cash balances that are more than 10 percent of the total assets of the company. A random sample of n = 100 companies shows that 13 had cash balances of more than 10 percent of assets. Based on this information, develop and interpret a 90 percent confidence interval estimate for the population proportion.
33. The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses. They selected a sample of 10 men and 10 women for the study. The sample results are:
n1 = 10 students n2 = 10 students
[pic] = 2.7 hours [pic] = 2.4 hours
s1 = .30 hours s2 = .40 hours
Using these results calculate (by filling in the following blanks) a 99%
confidence interval for the difference between the two population means. Assume
that the population variances are equal.
d. f. = -------------------- Critical value. = -----------------------------
Point estimate = ----------------------- Standard error of the estimate = -------------------
Margin of error = --------------------
Lower limit of the interval = -------------- Upper limit of the interval = ---------------
34. A major manufacturer of home electronics is interested in determining whether customers have a preference between two new speaker designs for their home entertainment centers. To test this, the design department manager has selected a random sample of customers and shown them the first design. A second sample of customers is shown design 2. The manager then asks each customer whether they prefer the new design they were shown over the one they currently own. The following results were observed:
Design 1 Design 2
Sample size n1 = 150 n2 = 80
Number preferring new x1 = 65 x2 = 58
Based on these data calculate (by filling in the following blanks) a 98% confidence interval for the difference between two proportions of design 1 and design 2.
Critical value. = -------------------------- Point estimate = ----------------------------
Standard error of the estimate = ------------------ Margin of error = --------------------
Lower limit of the interval = ---------------- Upper limit of the interval = ---------------
35. In a recent report, it was stated that the proportion of employees who carpool to their work is 0.14 and that the standard deviation of the sampling proportion is 0.0259. However, the report did not indicate what the sample size was. What was the sample size?
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