Part I.
Question 1. A 90% confidence interval estimate shows that there is a 90 percent chance that the true population value may fall within the range defined by the upper and lower limits.
Question 2. If a random variable is discrete, it seems that the outcome for the random variable will take on only one of two possible values.
Question 3. When people fail to respond to a survey, the data collection process can suffer from nonresponse bias.
Question 4. When stratified random sampling is employed, the population have to first be divided into homogeneous subgroups. Then either a systematic or a simple random sampling is done in every group to get the stratified sample.
Question 5. The primary application for the hypergeometric probability distribution is in situations where the sampling is done without replacement from a finite population.
Question 6. If the value of one discrete random variable increases, while the value of a second discrete random variable leads to decrease, these two variables are said to be uncorrelated.
Part II. Circle the best answer to the questions below.
Question 7. On the basis of data supplied by the U.S. Census Bureau, the Dalton Company has recently take a decision to build a new plant in Denver. For the Dalton Company, these data are examples of:
a. valid data.
b. secondary data.
c. primary data.
d. census data.
Question 8. The human resources department at a high tech company plans to implement an employee satisfaction study by sampling 100 employees from the 3,000 total employees. They plan to use systematic random sampling since the employee file is in alphabetic order. The first employee selected in the study should be:
a. the 30th employee.
b. employee 1 to 100 randomly selected.
c. employee 1 to 30 randomly selected.
d. employee 1 to 3000 randomly selected.
Question 9. The Subsequent probability distribution has been assessed for the number of accidents that happen in a Al Khobar city each day:
Accidents Probability
0 0.25
1 0.30
2 0.20
3 0.15
4 0.10
This distribution is a illustration of a(an):
a. Poisson distribution.
b. expected value distribution.
c. continuous probability distribution.
d. discrete probability distribution.
Question 10. When a customer enters a store there are two outcomes that may occur: (A) buy nothing or (B) buy some amount. In taht situation, if a customer buys some amount, he or she cannot also buy nothing. Thus the events A and B are:
a. mutually exclusive.
b. common.
c. independent.
d. dependent
Question 11. Which of the subsequent statements is not consistent with the Central Limit Theorem?
The Central Limit Theorem
a. applies to non-normal distributions.
b. applies without regard to the size of the sample.
c. Shows that the sampling distribution will be approximately normal.
d. Shows that the mean of the sampling distribution is equal to the population mean.
Question 12. A package delivery service claims that no more than 5% of all packages arrive at the address late. Consider that the conditions for the binomial hold, if a sample of size 10 packages is randomly selected and the 5% rate holds, what is the probability that more than 2 packages will be delivered late?
a. 0.0116
b. 0.0862
c. 0.0105
d. None of the above.
Question 13. You are given the subsequent sample data:
23 34 11 40 25 47
The standard deviation is approximately
a. 840
b. 160
c. 140
d. 12.96
e. 11.83
Question 14. The subsequent probability distribution has been assessed for the number of accidents that occur in a Al Khobar city each day:
Accidents Probability
0 0.20
1 0.25
2 0.15
3 0.30
4 0.10
Which of the subsequent is the probability that at least 2 accidents occur?
a. 0.25
b. 0.30.
c. 0.45.
d. 0.55.
Question 15. A random sample of 340 people in Riyadh showed that 66 listened to MBC-FM, a radio station in North Riyadh City. Based on this given information, what is the point calculatiuon for the proportion of people in Riyadh who listen to MBC-FM?
a. 340
b. 0.34.
c. 0.194
d. Can't be determined without knowing the desired confidence level.
Question 16. If the population variances are defined in an application where a manager wishes to estimate the difference between two population seems, the 95% confidence interval estimate will be developed using which of the following critical values:
a. z = 1.96.
b. z = 1.645.
c. t0.05 value with df = n1 + n2 - 2.
d. t0.05 value with df = .
Question 17. Consider it is known that the ages of all employees working for King Fahd University of Petroleum and Minerals is normally distributed with a mean of 44.2 and standard deviation of 5.6 years. Which of the following explains what the sampling distribution for looks like? will be distributed
a. normally with mean μk= 44.2 and standard error σx = 5.6/√n
b. normally with mean μx = 44.2 and standard deviation σx = 5.6
c. approximately normally with mean μx = 44.2 and standard error σx = 5.6/√n
d. approximately normally with mean μx = 44.2 and standard deviation σx =5.6
Part III. Solving Questions. You MUST show the key steps to a problem to maximize credit for your answers. You may shorten some steps to save time as long as the main steps are shown.
Question 18. The following data indicates the Stem-and-Leaf plot for price-earnings (P/E) ratios for the shares of 30 different companies.
Stem-and-leaf of P/E Ratio n = 30
Stem Unit = 1 (Leaf Unit = 0.1)
|
Stem
|
Leaf
|
Frequency
|
|
5
|
4 6
|
2
|
|
6
|
|
|
|
7
|
3
|
1
|
|
8
|
5
|
1
|
|
9
|
6 8 9
|
3
|
|
10
|
|
|
|
11
|
7 8
|
2
|
|
12
|
6
|
1
|
|
13
|
|
|
|
14
|
6 6
|
2
|
|
15
|
3 4 8
|
3
|
|
16
|
3 7 9
|
3
|
|
17
|
2 3 9
|
3
|
|
18
|
4 6
|
2
|
|
19
|
1
|
1
|
|
20
|
2 3
|
2
|
|
21
|
|
|
|
22
|
|
|
|
23
|
3 4
|
2
|
|
24
|
3 5
|
2
|
a. Determine the median price earning ratios.
(15.8+16.3)/2= 16.05
b. Determine the 70th percentile?
Data position is at 70/100(30+1) = 21.7. P70 = 23 + 0.7(29-23)= 23+ 4.2 = 27.2
Question 19. The Grocery Manufacturers of Saudi Arabia reported that 76% of consumers read the ingredients listed on a product's label. Consider the population proportion is p = .76 and a simple random sample of 400 consumers is selected from the population.
a. Explain the sampling distribution of the sample proportion .
b. What is the probability that the sample proportion will be within ± 0.03011 of the population proportion?
Question 20. The population standard deviation of P/E (price per earning) ratios for the stocks listed on the New York Stock Exchange (NYSE) is σ = 7.8 (The Wall Street Journal, January 20, 2000). Considered that we are interested in estimating the population mean P/E ratio for all stocks listed on the NYSE with 94.26% confidence. How various stocks should be included in the sample if we want a margin error of 2?
Question 21. In an effort to calculate the mean amount spent per customer for dinner at a major Dhahran restaurant, data were collected from a sample of 49 customers. Assume the population standard deviation is $5.
a. Determine the standard error of the mean?
b. At a 95% confidence level, evaluate the margin of error?
c. If the sample mean is $34.80, construct the 95% confidence interval for the population mean?
Question 22. For auditing purposes, Master's Accounting Firm collected a random sample of the accounts payable to the east and west branch offices of Amalgamated Distributors. The sample statistics obtained were :
Sample East Office West Office
size n 15 10
mean $300 $270
standard deviation s 16 20
a. Give a point estimate of the difference between means from the East and West branch offices of Amalgamated Distributors?
b. Considering equal variances, develop a 90% confidence interval for the difference between mean accounts payable at the two branches of Amalgamated Distributors?
c. Interpret your results in part b.
d. If you have the subsequent data instead (notice that the west office standard deviation is 149 while other values are the same),
Sample East Office West Office
size n 15 10
mean $300 $270
standard deviation s 16 149
Compared to parts a and b above, show how your 90% confidence interval changes with regards to each of the following:
1) Point estimate =
- does not change or - changes to ________________
2) Critical value
- does not change
- changes to zα/2 = _________ with α = __
- changes to tα/2 with α =__ 0.10 and df = ____ ugly formula
3) Standard error
- does not change or - changes to _____________
Question 23. A marketing research firm has come up with two coupon designs that provide credit card customer membership in a travel club. The research firm is interested in estimating the difference in proportion of customers who will join the club after receiving one of the two coupons. To get this estimate, the research firm sent out coupon design A to a random sample of 100 customers and coupon B to a second random sample of 100 customers. For coupon A, 11 customers joined the travel club, while 15 customers who received coupon B joined. Based upon this sample information,
a) Prepare the desired 99 percent confidence interval estimate.
b) interpret your results in part (a).