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Some MCQs on statistics

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1. Binomial Distribution
A fair die is rolled nine times. What is the probability that an odd number (1,3 or 5) will occur less than 3 times?
a) .0899
b) .2544
c) .7456
d) .9101

4. Binomial Distribution
This problem is a modified version of problem 8 in chapter 11. An automaker has issued a recall for truck transmissions. It has found 30% of its transmissions to be defective, and has issued a recall asking consumers to take their truck to their dealer. The Friendly Auto Mart sold 10 of these trucks, but has only 3 transmissions in stock. What is the probability that the auto dealer will need to order more transmissions? You should take your calculations to 4 decimal places.
a) .2335
b) .3504
c) .3838
d) .6496

5. Normal Distribution
The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels?
a) 0.0228
b) 0.0475
c) 0.0485
d) 0.0500

7. Decision Making without Probability (10.0 points)
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code.

If he uses the maximin criterion, how many new workers will he hire?
a) 1
b) 2
c) 3

9. Decision Tree Calculations
Consider the following decision tree.

What is the value associated with node 3?
a) 600
b) 1600
c) 1800
d) 2500

13. Random Number Generation

If a simulation begins with the first random number, what would the first simulation value be? (Hint: The random numbers are chosen from 0 - 100 with uniform distribution, so divide each random number by 100.)
a) 1
b) 2
c) 3
d) 4

14. Random Number Generation
Given this frequency distribution, the random number 0.61 would be interpreted as a demand of:

a) 0
b) 1
c) 2
d) 3

18. Moving Average Method
The following data summarizes the historical demand for a product

Determine the average forecast error when using the 4-month moving average method.
a) 5.25
b) 5.75
c) 6.25
d) 6.75

23. Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?
a) Trend only
b) Seasonal only
c) Trend plus seasonal
d) Trend plus random

26. Consider the following annual sales data for 1996-2003, use the linear regression method and determine the estimated sales equation,

NOTE: This question was taken from a test bank and the test publisher did not use the actual year as the x-value. You should replace 1996 with 1, 1997 with 2, 1998 with 3, and so on. These x-values will lead you to the correct answer. This technique is also commonly used in real world examples.
a) y = 2.63 + 0.21x
b) y = 2.63 - 0.21x
c) y = -0.21 + 2.63x
d) y = 0.21 - 2.63x

27.Consider the following annual sales data for 1996-2003. This is the same table of data shown on the previous question. Again, please replace 1996 with 1, 1997 with 2, 1998 with 3, etc.
Using year values of 1 through 8 instead of 1996 through 2003, determine the percent of variation of sales that is caused by the year number (1-8). The answers below are rounded to the nearest tenth, but are far enough apart so your correct answer will be close to only one answer below.

a) 91.54%
b) 93.22%
c) 95.34%
d) 96.55%

28. The law firm of Dewey, Cheetham, and Howe has a pool of candidates wishing for internship in the law firm. The law firm has decided to test each candidate on his or her ability to win a nuisance lawsuit. Candidates who score in the top 33% will be given an internship. The law firm has issued similar tests in the past and knows that the average score is 80 (out of 100), the standard deviation is 10, and that test scores are normally distributed. What is the minimum score that a candidate must earn in order to place in the top 33%?
a) 81.25
b) 84.40
c) 86.30
d) 88.60

30. This question requires some thought, but the correct answer can be reached if you think long enough about it.
You are performing an analysis of your chosen forecasting method and have tracked errors for forecasts over the previous 24 time periods. You have obtained the following results from your error analysis:
MAD = 25
MAPD = 0.10
E (Cumm. error) = 5
What might you conclude about your forecasts?
a) Forecasts are consistently above the actual demand.
b) Forecasts are consistently below the actual demand.
c) Forecasts fluctuate wildly above and below the actual demand.

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Hi

Please find attached the answers with explainations for your questions.

I am not able to attach files so i am pasting the word file here. You will get answers to the questions here. I am sending the files to Brainmass so that they can forward the files to you.

Regards

Unless otherwise instructed, you should carry your calculations to 4 decimal places and then round your answer accordingly. Note that round-off errors can still occur, even if you are doing the problem correctly. This may result in your answer being 0.01, 0.001, or 0.0001 off the actual correct answer. Do not panic if this is the case. The multiple-choice answers are far enough apart that the closest answer should be obvious.

For your decision analysis questions, please make sure you know the difference between expected value GIVEN perfect information and expected value OF perfect information.

1. Binomial Distribution
A fair die is rolled nine times. What is the probability that an odd number (1,3 or 5) will occur less than 3 times?
a) .0899
b) .2544
c) .7456
d) .9101
In Binomial Distribution, Probability of r successes in n trials is given as:
P(r)=P(r)=nCr p^r *q^(n-r)
nCr= nCr= n!/r!(n-r)!
p = probability of a success=0.5
q = 1- p = probability of a failure=0.5
n = number of trials=9
r = number of successes in n trials

P(r<3)=P(r=0)+p(r=1)+P(r=2)
P(r=0)=9C0 (0.5)^0 (0.5)^9 =0.00195
P(r=1)=9C1 (0.5)^1 (0.5)^8 =0.0176
P(r=2)=9C2 (0.5)^2 (0.5)^7 =0.0703
Thus, P(r<3)=0.00195+0.0176+0.0703=0.08984
Thus, answer (a)

4. Binomial Distribution
This problem is a modified version of problem 8 in chapter 11. An automaker has issued a recall for truck transmissions. It has found 30% of its transmissions to be defective, and has issued a recall asking consumers to take their truck to their dealer. The Friendly Auto Mart sold 10 of these trucks, but has only 3 transmissions in stock. What is the probability that the auto dealer will need to order more transmissions? You should take your calculations to 4 decimal places.
a) .2335
b) .3504
c) .3838
d) .6496

P(r)=nCr p^r *q^(n-r)
nCr= n!/r!(n-r)!
p = probability of a ...

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Descriptive statistics: 18 multiple choice questions

Assignment: Week 1 Ch 1

1. A quality-control manager randomly selects 90 bottles of vinegar that were filled on September 21 to assess the calibration of the filling machine.
What is the population in the study?
A. Bottles of vinegar produced in the plant.
B. Bottles of vinegar produced in the plant on September 21.
C. The 90 bottles of vinegar produced in the plant on September 21.
D. The 90 bottles of vinegar produced in the plant.

What is the sample in the study?
A. The 90 bottles of vinegar produced in the plant in September.
B. Bottles of vinegar produced in the plant on September 21.
C. Bottles of vinegar produced in the plant.
D. The 90 bottles of vinegar in the plant on Sept. 21.

2. Determine whether the numerical value is a parameter or a statistic. Explain your reasoning.
A Survey of 42 out of hundreds in a dining hall showed that 17 enjoyed their meal.
Choose the correct answer below.
A. Statistic, because the data set of all people in the dining hall is a sample.
B. Parameter, because the data set of all people in the dining hall is a sample.
C. Parameter, because the data set of 42 people in a dining hall is a sample.
D. Statistic, because the data of 42 people in a dining hall is a sample.
E. Parameter, because the data set of all people in the dining hall is a population.
F. Statistic, because the data set of all people in the dining hall is a population.
G. Statistic, because the data set of 42 people in a dining hall is a population.
H. Parameter, because the data set of 42 people in a dining hall is a population.

3. Suppose a survey of 558 women in the United States found that more than 605 are the primary investor in their household. Which part of the survey represents the descriptive branch of statistic?
Make an inference based on the results of the Survey.
Choose the best statement of the descriptive statistic in the problem.

A. There is an association between the 558 women and being the primary investor in their household.
B. 538 women were surveyed
C. 60% of women in the sample are the primary investor in their household.
D. There is an association between the 538 women and being the primary investor in their household.

Choose the best inference from the given information.
A. 538 women were surveyed.
B. 60% of women in the sample are the primary investor in their household.
C. There is an association between the 538 women and being the primary investor in their household.
D. There is as association between U.S. women and being the primary investor in their household

4. A study shows that students in first grade are shorter than students in fourth grade.
(a) Make an inference based on the results of the study. Choose the correct answer below.
(b) What might this inference incorrectly imply?
A. Students in first grade have not taken enough vitamins to grow yet.
B. Students in first grade are younger than the students in fourth grade and have grown less.
C. Students in fourth grade are shorter than students in first grade.
D. Students in first grade are shorter than students in fourth grade.

(c) What might this inference imply?
A. This inference may incorrectly imply that if you switched to fourth grade, you would be shorter than you would be if you were in the first grade.
B. This inference may incorrectly imply that students in first grade have not taken enough vitamins to grow yet.
C. This inference may incorrectly imply that students in first grade are younger than the students in fourth grade and have grown less.
D. This inference may incorrectly imply that if you switched to the first grade, you would be shorter than you would be if you were in the fourth grade.

5. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A population is the collection of some outcomes, responses, measurements, or counts that are of interest.
Choose the correct answer below.
A. True.
B. False. A population is the collection of all outcomes, responses, measurements, or counts that are interest.
C. False. A sample is the collection of all outcomes, responses, measurements, or counts that are of interest.

6. Determine whether the variable is qualitative or quantitative.
Distance in miles to nearest outdoor stadium.
Is the variable qualitative or quantitative?
( ) Qualitative
( ) Quantitative

7. The following appear on a physician's intake form. Identify the level of measurement of the data.
(a) Family history of illness
(b) Happiness level ( scale of 0 to 10)
(c) Temperature
(d) Time since last visit

(a) What is the level of measurement for "family history of illness"?

( ) Ordinal
( ) Interval
( ) Nominal
( ) Ratio

(b) What is the level of measurement for "Happiness level (scale of 0 t0 10)?
( ) Ordinal
( ) Ratio
( ) interval
( ) Nominal

(c) What is the level of measurement for Temperature"?
( ) Ordinal
( ) ratio
( ) Interval
( ) Nominal

(d) What is the level of measurement for "Time since last visit"?
( ) Interval
( ) Ration
( ) Nominal
( ) Ordinal

8. Determine whether the statement is true or false. If is false, rewrite it as a true statement.
More types of calculation can be performed with data at the interval level than with data at nominal level.
Choose the correct answer below.
( ) A. False. More types of calculations can be performed with data at interval level than with data at the nominal level
( ) B. True.
( ) C. False. The same types of calculations can be performed with data at the nominal level and with data at the interval level.

9. Decide which method of data collection you would use to collect data for the study
A study of the effect on the taste of a snack food made with a fat substitute.
Choose the correct answer below.
A. Simulation
B. Experiment
C. Survey
D. Observational Study

10. Decide which method of data collection you would use to collect data for the study described below.
A study of how fast a certain poison kills a human child.
Choose the correct answer.
A. Observational study
B. Simulation
C. Experiment
D. Survey

11. A Radio station asks its listeners to call in their opinion regarding the use of pesticides in residential areas.
What type of sampling is used?
A. Systematic
B. Simple random
C. Convenience
D. Stratified
E. Cluster

12. To determine customer opinion of their service, Business Depot randomly selects 120 stores during a certain week and surveys all customers present in the store.
What type of sampling is used?
A. Stratified
B. Convenience
C. Simple random
D. Systematic
E. Cluster

13. Nissan wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 70 customers and asks them about their level of satisfaction with the company.
What type of sampling is used?
A. Cluster
B. Systematic
C. Simple random
D. Stratified
E. Convenience

14. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods selects every 20th soup can that comes of the assembly line starting with the tenth until she obtains a sample of 60 soup cans.
What type of sampling is used/
A. Cluster
B. Systematic
C. Simple random
D. Convenience
E. Stratified

15. To determine her blood pressure, Jean divides up her day into three parts, morning, afternoon, and evening. She then measures her blood pleasure at 3 randomly selected times during each part of the day.
What type of sampling is used?
A. Stratified
B. Convenience
C. Simple random
D. Systematic
E. Cluster

16. Determine whether you would take a census or use sampling to collect data for the study described below.
The most popular house color among the 20 employees of a company.
Would you take a census or use a sampling?
( ) Census
( ) Sampling

17. Determine whether the survey question is biased. If the question is biased, suggest a better wording.
Why is eating eggs bad for you?
Is the question biased?
( ) No
( ) Yes

If the question is biased, which question below is worded better?
A. Do you think that eating eggs is bad for you?
B. How do you think eating eggs affects your health?
C. The original question is not biased.
D. Why is eating eggs good for you/
E. Do you think that eating eggs is good for you?

18. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals.
Choose the correct answer below.
A. True
B. False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals.
C. False. The method for selecting a cluster sample is to order a population in some way and then select members of the population at regular intervals.

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