Activity X: EVALUATING YOUR STATISTICAL LITERACY
1.Attack or defend the following statements:
a.The standard deviation for yearly income in France is $4000 and for Germany it is $8000. Hence income in Germany is more variable than that in France.
b.Because 40% of the voters favor Bush’s stand on the environment, if we select 10 voters at random, 4 of them will support Bush's stand on the environment.
c.A larger sample will always guarantee us a better estimate of what is true of the entire population.
d.If two distributions have exactly the same mean and standard deviation, their frequency curves (probability distribution) will be identical.
e.If the mean in a test is 65 and the standard deviation is 5, it would be very unlikely to have a test score of over 70.
f.Stratified samples are always better than random samples.
g.In sampling, if we look at 1000 people when the population is 1 million, we will look at 3000 people when the population is 3 million.
h.A study shows that 70% of the customers like hamburgers, 60% like French fries, and 10% like both. Do you accept the study? Explain.
i.A study concludes that the population of students is Normally distributed with a mean age of 30 years and a median age of 25 years. Do you accept the study? Explain.
2.Identify the following data as nominal, ordinal, interval or ratio.
a.Numbers on football jerseys
b.Temperature in a room
c.Income of sales people
d.Ranking of tennis players
3.The underlined number is either a parameter or a statistic. Explain which each is:
A telephone sales outfit in L.A. uses a device that dials phone numbers in the city at random. Of the first 100 numbers dialed, 23 are unlisted. This is not surprising since 38% of all L.A. residential numbers are unlisted.
23 –
38% -
4.Explain the difference between Data, Information, and Knowledge.
5.In the context of the following problem, explain how the terms or symbols listed below pertain to the problem.
A company wishes to estimate what its current customers plan to spend on new products during the next year. They currently have 2500 customers. The company is particularly interested in estimating the total sales for next year. A random sample of 100 customers is taken and it is determined that the average amount customers will spend next year is $2000 with a standard deviation of $100. The histogram is approximately normal.
a.Population of interest
b.Random Variable of interest
c.µx
d.
e.Sx
f.Why would a random sample not be appropriate? Explain how and why you would have stratified the sample.
g.Discuss how sampling errors might occur.
h.If the total number of customers the company has is 2500, how would you estimate the total sales?
i.If you were the marketing manager, how would your "strategies" change on how you would assign your sales force if the study had shown: Average is $2000, standard deviation is $10,000 and probability distribution is skewed to the right?
j.In taking the actual measurements, (talking with customers) discuss what the following terms mean in the context of the problem:
accurate measurements:
reliable measurements:
precise measurements:
k.If the average had been stated at $1987.13, would you have reacted to this differently than you would have to the $2000 figure?
6.A company believes that its sales depend on its level of advertising. It conducts a study trying various levels of advertising. It spends 20,000 the first week and increases the spending by 10,000 for 5 weeks. In doing a simple linear regression in sales vs. advertising, the company finds the slope is 3 and the
y-intercept is $100,000.
a.Independent variable x =
b.Dependent variable y =
c.Best Fitting Least Square Line = y =
d.Using the above model, predict sales if $20,000 is spent on advertising.
If $100,000 is spent on advertising?
Do you have the same faith in both estimates? Explain.
e.Give an interpretation of the slope in the context of the problem.
f.Give an interpretation of the y-intercept in the context of the problem.
7.For each of the following statements, you can ask one more question. What would it be? Give a different question for each statement.
a.There appears to be a 30% chance of catching the flu this year.
b.The study of 100 medical doctors in Minnesota showed an average salary of $120,000. (Assume a random sample.)
c.A man is told that he has cancer and that it is terminal. The median number of years that he will survive is 5 years. This is based on a study of 200,000 patients with a similar cancer.
d.Your lawyer states there is a 90% chance that you will win the case.
8.Systems Thinking
A company is interested in marketing a new device that measures blood pressure. At the present time accounting indicates they have $2 million invested in R & D in the product. Production indicates that the cost of producing the device is $70 for material and $80 for labor per device. It will take 3 months to set up the production facilities at a cost of $3 million. Marketing feels that there is a potential market of 20 million people if the price is kept under $200. They know of at least 2 other companies that are within 6 months of marketing the device at a price close to $200. Also, the company has just suffered a major financial setback because of a patent infringement case and cash flow is a major concern. You have to decide if you should or should not produce and market the device. It's your decision.
- What are the consequences of an incorrect decision?
Use the Type I—Type II Error Model for your discussion. Be a Systems Thinker in your discussion.
Real LifeProduct Sells / Product Doesn’t Sell
Correct Decision / Type II Error
Type I Error
/ Correct Decision
Type I—Type II Error Model
b.Of the numbers given above, select the one you would have the least faith in its accuracy. Explain your selection.
c.Which of the numbers given above do you have the most faith in its accuracy? Explain.
d.Select a number that you feel the reliability of the number may be of concern. Select a different value than that picked in b. Explain your selection.
e.Discuss the importance of accuracy of the data when considering the break-even point. Remember the break-even point is where Revenue = Cost. Does it make sense to use a point estimate? Explain.
For the problemR = 200X
C = 150X + 5,000,000
- Is there a logic error in the cost equation? Explain.
- If you could get additional data/information, describe what data and information that would be, where you would get it, and how you would get it.
- Professor Sadistic of the Statistics Department, you are told by a friend, failed 50% of her class last semester. What two questions would you ask to evaluate this statement?
10.Hand Gun Control has published the following statement: "In the U.S. during a one-year period, 11,586 murders were committed using a handgun; during a similar period of time in Japan there were 77 murders using handguns, in Australia 7 murders, in Switzerland 24 murders". Assume you are the publicity director for the National Rifle Association, how would you "attack" these figures?
11.A company is considering paying a known celebrity $2 million over the next year to endorse their product. The President of the company has decided, before a deal is agreed upon, that the company should get some feeling for how this endorsement will affect sales.
a.Define the population of interest.
b.Explain how you would determine if the celebrity is worth the $2 million.
c.Discuss the issue of accurate, reliable and precise measurements as they relate to the measurements in part b.
12. Using the following sample data (6, 9, 9, 3, 5, 9, 2, 5) find the:
(show work)
a.arraya)
b.meanb)
c.medianc)
d.moded)
e. rangee)
f.variancef)
g.standard deviationg)
h.sample sizeh)
i.average deviationi)
j.Coefficient of Variationj)
Activity X - 1
Spring 2002