Question 6 (04 + 03 + 03 = 10 Marks) 6) What is sampling error and why is it not present in a survey of a population? Stratified random sampling reflects Pareto’s 80:20 Principle. Discuss how stratified random sampling can make audit sampling (e.g. for accounts receivable (A/R), inventory, or payroll) more cost-effective. What is the main statistical downside of stratified random sampling?
In: Statistics and Probability
A coffee manufacturer is interested in whether the mean daily consumption of regular- coffee drinkers is less than that of decaffeinated coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.21 cups per day and 1.40 for those drinking decaffeinated coffee. A random sample of 54 regular coffee drinkers showed a mean of 4.59 cups per day. A sample of 49 decaffeinated coffee drinkers showed a mean of 5.64 cups per day.
a) Is this a One-tailed or Two-tailed test?
b) State the decision rule
c) Compute the value test statistic
d) What is the p-value
e) What is the decision (reject or do not reject)
In: Statistics and Probability
Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 55% of all people who take the state bar exam pass. Let n = 1, 2, 3, ... represent the number of times a person takes the bar exam until the first pass.
(a) Write out a formula for the probability distribution of the
random variable n. (Use p and n in your
answer.)
P(n) =
(b) What is the probability that Bob first passes the bar exam on
the second try (n = 2)? (Use 3 decimal places.)
(c) What is the probability that Bob needs three attempts to pass
the bar exam? (Use 3 decimal places.)
(d) What is the probability that Bob needs more than three attempts
to pass the bar exam? (Use 3 decimal places.)
(e) What is the expected number of attempts at the state bar exam
Bob must make for his (first) pass? Hint: Use
μfor the geometric distribution and round.
In: Statistics and Probability
During a study group, you and your friend discover that you have arrived (independently) at different solutions to a math problem. From past experience, you know that you generally answer questions correctly 75% of the time, but your friend answers questions correctly 90% of the time.
a) In general, how often does it happen that you answer a question correctly and your friend answers incorrectly?
b) In general, how often does it happen that you answer a question incorrectly and your friend answers correctly?
c) In general, how often does it happen that one of the two of you answers a question correctly and the other answers incorrectly?
d) The TA confirms that one of your two answers is correct, but refuses to say whose. What is the probability that yours is the correct answer?
In: Statistics and Probability
In: Statistics and Probability
1.You go to a casino with $31 and the following strategy: In the first round you bet $1, if you win, you receive double your bet, you leave. If you lose you double your bet to $2. You continue this strategy that you receive double your bet and leave if you win, and doubling you bet in the previous round if you lose, until you run out of money. Let X equal the total amount of money you win (”winning” a negative amount of money is the same as losing that amount). If the probability of winning in each round is independent and equal to 9/20:
(a) What is the pmf, pX(x), of X?
(b) What is E[X] and Var[X]?
2. You are dealt one card from a full deck of 52 cards and your opponent is dealt two cards (without replacement). If you get a face card (jack, queen or king) your opponent pays you 5, if you get an ace your opponent pays you 2. If you don’t have a face card or an ace, but you have a spade and your opponent doesn’t have a spade they pay you 1. In all other cases you pay 1. What is the expectation of your winnings?
In: Statistics and Probability
|
Time (days) |
Immediate |
Time (days) |
Immediate |
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|
Activity |
a |
m |
b |
Predecessor(s) |
Activity |
a |
m |
b |
Predecessor(s) |
||||||
|
A |
55 |
55 |
77 |
long dash— |
H |
44 |
44 |
66 |
E, F |
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|
B |
11 |
22 |
55 |
long dash— |
I |
22 |
77 |
1010 |
G, H |
||||||
|
C |
55 |
55 |
55 |
A |
J |
22 |
44 |
77 |
I |
||||||
|
D |
44 |
88 |
1313 |
A |
K |
66 |
1010 |
1313 |
I |
||||||
|
E |
11 |
1010 |
1717 |
B, C |
L |
22 |
66 |
66 |
J |
||||||
|
F |
11 |
55 |
77 |
D |
M |
22 |
22 |
33 |
K |
||||||
|
G |
22 |
66 |
99 |
D |
N |
77 |
77 |
1212 |
L, M |
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b) If the time to complete the activities on the critical path is normally distributed, then the probability that the critical path will be finished in 55 days or less =
In: Statistics and Probability
In: Statistics and Probability
In this project, you will collect data from real world to construct a multiple regression model. The resulting model will be used for a prediction purpose. For example, suppose you are interested in “sales price of houses”. In a multiple regression model, this is called a “response variable”. There are many important factors that affect the prices of houses.
Those factors include size (square feet), number of bedrooms, number of baths, age of the house, distance to a major grocery store. The factors (or variables) which are used for a multiple regression model are called “explanatory variables” (or “independent variables”). Good choice of explanatory variables is one of the most important steps to construct a good multiple regression model. www.zillow.com, One of the most recognized realtor website in United States, provides predicted prices (“zestimate”) of houses. Now the goal of the project is to construct your own prediction model of house prices. The first step of the project is to decide which explanatory variables you will use. In this project, please find at least four explanatory variables.
Next step is data collection. You are required to collect at least 100 observations (samples). Otherwise, you will not get full credits. Each observation must include sales value and all the values of explanatory variables of your choice. For example, if your explanatory variables are size, number of beds, number of baths, and age of houses, then the data set must be of the following form
In: Statistics and Probability
| 4. In order to test whether brand-name printer cartridges produce more printed pages, on average, than generic cartridges, a research firm has 6 randomly selected printer users use both types of cartridges and record how many pages were printed with each. The number of pages printed for each user by each type of cartridge are shown. | |||||||||||||||||||||||||||||||||||||
| Use the 0.01 significance level to test whether the brand-name cartridges print more pages on average than the generic cartridges. | |||||||||||||||||||||||||||||||||||||
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Identify and interpret the p-value for the test.
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In: Statistics and Probability
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A telephone sales solicitor, trying to decide between two alternative sales pitches, randomly alternated between them during a day of calls. Using approach A, 20% of 100 calls led to requests for the mailing of additional product information. For approach B in another 100 calls, only 14 % led to requests for the product information mailing. At the 0.05 significance level, can we conclude that the difference in results was due to chance? Construct the 95% confidence level for the difference between population proportions (π1 - π2). Identify and interpret the p-value for the test. |
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In: Statistics and Probability
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To prevent E. coli, meat should be cooked to an internal temperature of at least 160°F. However, different meat patties cooked for the same amount of time will have different final internal temperatures because of variations in the patties and variations in burner temperatures. A regional hamburger chain plans to replace its current burners with one of two new digitally controlled models. If there is a significant difference in the variance of the two models, the chain will select the model with the smaller variance in the final internal meat temperature. The chain's purchasing directors have arranged to randomly sample 11 patties cooked by burner model 1 and 13 cooked by burner model 2.
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In: Statistics and Probability
When and how do you use a chi-square distribution to test if two
variables are independent? What is an example of how to use the
contingency table to find expected frequencies?
In: Statistics and Probability
Simple linear regression, like ARIMA, involves statistical modeling. Unlike decomposition, averaging and smoothing methods, fitting a simple linear regression model to data involves statistical inference.
Moreover, several assumptions/conditions need to be satisfied in order to use a simple linear regression model. One might think that this added level of complexity would make regression analysis less likely to be used in practice. On the contrary, it is widely used by management. Why do you suppose this is the case? What advantages does simple linear regression have over the forecasting methods we've covered so far? Can you give an example of how simple linear regression may be used in your area of employment and/or expertise?
In: Statistics and Probability
According to the Consumer Electronics Manufacturers Association, 10% of all U.S households have a fax machine and 52% have a personal computer. Suppose 91% of all U.S households having a fax machine also have a personal computer. a. What is the probability that a randomly selected US household has a fax machine and a personal computer? b. What is the probability that a randomly selected US household has a fax machine or personal computer? c. What is the probability that a randomly selected US household has a fax machine and does not have a personal computer? d. Are the events fax machine and personal computer independent? Why?
In: Statistics and Probability