e - King Fahd University of Petroleum and Minerals

STAT 211 Business Statistics I 1 

KING FAHD UNIVERSITY OF PETROLEUM & MINERALS 

DEPARTMENT OF MATHEMATICAL SCIENCES 

DHAHRAN, SAUDI ARABIA 

STAT 211: BUSINESS STATISTICS I 

Semester 061 

Final Exam 

Saturday January, 27, 2007 

Please circle your: 

Instructor’s name & section number 

Dr. Ibrahim Rahimov 1 2 

Mr. Esam Al Sawi 3 4 5 

Name: ID# Serial# 

Question No Full Marks Marks Obtained 

1 

12 

2 

3 

4 

15 

9 

10 

5 10 

6 12 

7 12 

Total 

80


Q1. (12 pts.) True or False: 

STATEMENT 

T/F 

1. Statistics is the science of collecting, summarizing, analyzing, and drawing 

conclusions. 

2. The primary tools used to draw inferences in statistics are charts and graphs. 

3. Open-ended questions are typically included in a survey when the objective is to 

provide the maximum opportunity for the respondent to express his or her opinion. 

4. Selection bias occurs when the respondent decides which of the questions on the 

survey to answer. 

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. Cluster sampling and stratified random sampling are essentially the same type of 

statistical sampling technique. 

7. Nominal data are typically considered to be qualitative. 

8. The data level that will provide the greatest flexibility when it comes to analyzing 

the data is nominal data. 

9. A variable which has all the properties of an interval variable, but also has a true 

zero, is a ratio level variable 

10. A qualitative variable can be either nominal or ordinal, but cannot be interval or 

ratio level. 

11. 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. 

12. Data collected on marital status (married, divorced, single, other) would be an 

ordinal level variable.


For Q2, write all your choices in this table: 

Question 

Answer 

Q1 a b c d 

Q2 a b c d 

Q3 a b c d 

Q4 a b c d 

Q5 a b c d 

Q6 a b c d 

Q7 a b c d 

Q8 a b c d 

Q9 a b c d 

Q10 a b c d 

Q11 a b c d 

Q12 a b c d 

Q13 a b c d 

Q14 a b c d 

Q15 a b c d


Q2. (15 pts.) Choose the correct answer for the flowing question: 

1. Consider the following chart. Which of the following statements is most correct 

140 

120 

100 

Y variable 

80 

60 

40 

20 

0 

0 5 10 15 20 25 30 35 

X variable 

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. 

2. A small company has 7 employees. The numbers of years these employees have worked for 

this company are shown as follows: 

4 14 3 16 9 8 16 

Based upon this information, the median number of years that employees have been with 

this company is: 

a. 9 years. 

b. 16 years. 

c. 10 years. 

d. None of the above. 

3. A sample of people who have attended a college football game at your university has a 

mean= 3.2 members in their family. The mode number of family members is 2 and the 

median number is 2.0. Based on this information: 

a. The population mean exceeds 3.2. 

b. The distribution is bell-shaped. 

c. The distribution is right-skewed. 

d. The distribution is left-skewed 

4. Which of the following measures is not affected by extreme values in the data 

a. The mean 

b. The median 

c. The range 

d. The standard deviation.


5. If the age distribution of customers at a major retail chain is thought to be bell-shaped with 

a mean equal to 43 years and a standard deviation equal to 7 years, the percentage of 

customers between the ages of 29 and 50 years is: 

a. Approximately 81.5. 

b. Approximately 68. 

c. At least 75. 

d. Approximately 95. 

6. A recent study in the restaurant business determined that the mean tips for male waiters per 

hour of work are $6.78 with a standard deviation of $2.11. The mean tips per hour for 

female waiters are $7.86 with a standard deviation of $2.20. Based on this information, 

which of the following statements do we know to be true 

a. The distribution of tips for both males and females is right-skewed. 

b. The variation in tips received by females is more variable than males. 

c. The median tip for females exceeds that of males. 

d. On a relative basis, males have more variation in tips per hour than do females. 

7. Which of the following statements is incorrect 

a. The expected value of a discrete probability distribution is the long-run average 

value assuming the experiment will be repeated many times. 

b. The standard deviation of a discrete probability distribution measures the average 

variation of the random variable from the mean. 

c. The distribution is considered uniform if all the probabilities are equal. 

d. The mean of the probability distribution is equal to the square root of the expected 

value. 

8. If events E and F are independent with P(E) = 0.3 and P(F) = 0.5, find P(E ∪ F). 

a. 0.35 

b. 0.65 

c. 0.80 

d. None of the above.


9. The following probability distribution has been assessed for the number of accidents that 

occur in a mid-western city each day: 

Accidents Probability 

0 0.25 

1 0.20 

2 0.30 

3 0.15 

4 0.10 

Based on this probability distribution, the mean of the number of accidents per day is: 

a. 2. 

b. 0.12. 

c. 1.65. 


10. A manufacturer produces thermostats, 10% of which are defective. From a production run, 

a sample of four thermostats is randomly selected. Determine the probability that three of 

the selected thermostats are defective. You may assume that the four trials are independent 

and that the number of defective items in the sample has a binomial distribution. 

a. 0.0035 

b. 0.0036 

c. 0.0037 

d. 0.0038 

11. If Z has a standard normal random variable and P(Z > a) = 0.9938, find P(a


13. Which of the following statements is not consistent with the Central Limit Theorem 

a. The Central Limit Theorem applies without regard to the size of the sample. 

b. The Central Limit Theorem applies to non-normal distributions. 

c. The Central Limit Theorem indicates that the sampling distribution will be 

approximately normal. 

d. The Central Limit Theorem indicates that the mean of the sampling distribution will 

be equal to the population mean. 

14. A Company produces frozen French fries that are then sold to customers such as 

McDonald’s. The “prime” line of fries has an average length of 6.00 inches with a 

standard deviation of 0.50 inches. To make sure that company continues to meet the 

quality standard for “prime” fries, they plan to select a random sample of n = 100 fries 

each day. Yesterday, the sample mean was 6.05 inches. What is the probability that the 

mean would be 6.05 inches or more if they are meeting the quality standards 

a. Approximately 0.235 

b. Approximately 0.3413 

c. Approximately 0.9413 


15. 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 

a. 100 

b. 180 

c. 460 

d. Can’t be determined without more information.


Q3. (4+5=9pts.) The president of a company believes that 30% of the firm’s orders come from new 

customers. A sample random sample of 100 orders will be used to estimate the true proportion of 

new customers. The results of the sample will be used to verify the president’s clime. 

a. Assume that the president is correct and P=0.30. What is the sampling distribution of p for 

this study 

b. What is the probability that the sample proportion p will be between 0.20 and 0.40 

---------------------------------------------------------------------------------- 

Q4. (2+4+4=10 pts.) In an effort to estimate the mean amount spent per customer for dinner at a 

restaurant, data were collected for a sample of 49 customers over a three-week period. Assume that 

the population standard deviation is $2.50. 

a. What is the standard error of the mean 

b. At the 95% confidence, what is the margin of error 

c. If the sample mean is $22.6, what is the 95% confidence interval for the population mean


Q5. (4+3+3=10 pts.) In the testing of a new production method 18 employees were selected 

randomly and asked to try the new method. The sample mean production rate for the 18 employees 

was 80 parts per hour and the sample standard deviation was 10 parts per hour. 

a. Provide 95% confidence intervals for the population mean. 

b. Comment on your answer. 

c. What assumptions you made to solve the problem


Q6. (2+6+4=12 pts.) CNN TV poll asked 814 adults to respond to a series of questions about their 

feelings toward the state of affairs within the USA. A total of 562 adults responded “Yes” to the 

question: “Do you feel things are going well in the United States these days” 

a. What is the point estimate of the proportion of the adult population who feel thing are going 

well in the USA 

b. What is the 90% confidence interval for the proportion of the adult population who feel thing 

are going well in the USA 

c. How large a sample would be necessary to estimate the true proportion of the adult who feel 

thing are going well in the USA within 3%, with 95% confidence Assume p =0.69.


Q7. (2+6+4=12 pts.) An urban planning group is interested in estimating the difference between the 

mean household incomes for two neighborhoods in a large area. Independent random samples of 

households in the neighborhoods provided the following results. 

Neighborhood 1 Neighborhood 2 

Sample size=8 

Sample size=12 

Sample mean=$15700 Sample mean $14500 

Sample St. Deviation=$700 Sample St. Deviation=850 

a. Find point estimate for the difference between the mean incomes in the two neighborhoods. 

b. Find a 95% confidence interval for the difference between the mean incomes. 

c. What assumptions were made to compute the interval estimate in part (b)


Some Useful Formulas 

• Sample standard deviation: 

S 

⎛ 

( x ) 2 ⎞ 

⎜ 2 ∑ 

2 ∑ x − ⎟ 

∑( − ) 

⎜ n ⎟ 

⎝ 

⎠ ∑ 

x x x − nx ( ) 

= = = 

n −1 n −1 n −1 

2 2 

• P( E or E ) = P( E ) + P( E ) − P( E and E ) 

1 2 1 2 1 2 

• Conditional Probability: P ( E E ) 

• Binomial: ( ) 

• Poisson: ( ) 

( E1and 

E2) 

P ( E ) 

P 

1 2 = 

2 

n! 

x n − x 

P x = pq , µ = E ( X ) = n p, 

σ = npq 

x! ( n− 

x! 

) 

x 

( λt 

) 

− t 

P x 

e λ 

= , µ = λt , σ = λt 

x ! 

• Hyeprgeometric: P( x ) 

• Uniform: f ( x ) 

If a c d b 

= 

C 

C 

N − X X 

n− 

x x 

N 

n 

C 

⎧ 1 

⎪ if a ≤x ≤b 

= ⎨b 

− a 

, 

⎪⎩ 0 otherwise 

≤ < ≤ P( c≤ X ≤ d ) = ( d − c) f ( x) 

P 0≤ x ≤ a = 1− 

e − λ a 

• Exponential: ( ) 

• Sampling Error = Statistics Value – Parameter Value. 

σ 

• µ x = µ , σx 

= 

n 

If the population is finite and sampling is without replacement σx 

• µ = p, 

σ 

p p 

p(1 − p) 

= , 

n 

If the population is finite and sampling is without replacement σ = 

p 

σ N− 

n 

= 

n N−1 

p(1− 

p) N − n 

n N−1


• Confidence interval estimate for µ ( σ known) 

x ± zα/2 

σ 

n 

• Confidence interval estimate for µ ( σ unknown ) x ± tα 

/2 

s 

n 

• 

2 2 

2 

zα/2 σ ⎛zα/2 

σ⎞ 

Required sample size: n = = 

2 ⎜ 

e e ⎟ 

⎝ ⎠ 

• Confidence interval for population proportion : p ± zα 

/2 

• Required sample size is: n = 

2 

α /2 

2 

z p(1 − p) 

e 

p(1 − p) 

n 

2 2 

σ1 σ2 

• The confidence interval for µ1 – µ2 ( ( σ1, σ 

2 

are known ) is:( x1 − x2 ) ± z α /2 + 

n1 n2 

• Ifσ1 and σ2 unknown, and we have large samples, then: The confidence interval for µ1 – µ2 

2 2 

s1 s2 

is:( x1 − x2 ) ± z α /2 + 

n1 n2 

• If σ1 and σ2 unknown, and small samples: ( ) 

( − ) + ( − ) 

1 1 2 2 2 

2 

1 1 

x1 − x2 ± t α /2 sp 

+ , where 

n n 

1 2 

n 1 s n 1 s 

sp 

= 

n1 + n2 

−2 

sd 

• Paired Samples: d ± t α /2 

n 

• The confidence interval for the difference between two population proportions 

p(1 

1 

p) 

1 

p 

2(1 p 

2) 

( p1 − p2) ± z − − 

α /2 

+ 

n n 

1 2

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