Reference no: EM132313836

Advanced Statistics Questions -

Odd or Even: You ask 45 people to choose a number between 1 and 10, and 33 of them choose an odd number. Estimate the probability that the next person you ask will choose an odd number. Round your answer to 3 significant digits*.

*Significant Digits: Here are some probabilities expressed to 3 significant digits.

You start counting digits from left to right starting with the first non-zero digit.

0.123   0.0123   0.00123   0.102   0.350   0.300

Life Insurance: A life insurance company wants to estimate the probability that a 40-year-old male will live through the next year. In a sample of 7000 such men from prior years, 6994 lived through the year. Use the relative frequency approximation to estimate the probability that a randomly selected 40-year-old male will live through the next year. Round your answer to 4 decimal places.

Weather Forecast: The table below indicates the accuracy of a local weather report with respect to rain or no rain over the past year. This table gives the results of 365 consecutive days and compares whether it rained or not to whether or not rain was predicted.

	Did it actually rain?
	Yes	No
Report Predicted Rain	100	20
Report Predicted No Rain	40	205

(a) How many times was the prediction correct?

(b) How many times was it wrong?

(c) If one day is randomly selected from last year, what is the probability that the prediction was correct? Round your answer to 3 significant digits*.

(d) Tomorrow, the same local weather report will be given. Estimate the probability that it will be correct with respect to rain or no rain. Round your answer to 3 significant digits*.

*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.

0.123   0.0123    0.00123    0.102    0.350   0.300

Sampling Methods: Classify the type of sampling method used.

A quality assurance person randomly selects one box of CD's coming off the production line and tests all of the CD's in that box for defects.

• systematic
• stratified
• cluster
• none of these

Does this qualify as a random sample?

• Yes
• No
• not enough information

Sampling Methods: Classify the type of sampling method used.

At a border crossing, every 15th car is searched.

• systematic
• stratified
• cluster
• none of these

Does this qualify as a random sample?

• Yes
• No
• not enough information

Random and Simple Random: In a group of 100 males and 200 females, 40 participants are selected for a survey: 20 males and 20 females.

This sampling method is which of the following?

• random but not simple random
• simple random
• neither

Grass Seed: In a 10-pound bag of Doug's grass seed, 94% of the seeds are actually grass seeds and the other 6% produce weeds. In a 10-pound bag of generic grass seed, only 83% of the seeds are actually grass seeds.

(a) How many pounds of grass seed are in a typical 10-pound bag of Doug's grass seed? Round your answer to 1 decimal place.

(b) How many pounds of grass seed are in a typical 10-pound bag of generic grass seed? Round your answer to 1 decimal place.

(c) Only one of the following statements is true. Which one is true?

• In a typical 10-pound bag, the generic grass seed contains 11.0% less grass seed than Doug's brand.
• In a typical 10-pound bag, Doug's grass seed contains 13.3% more grass seed than the generic brand.
• In a typical 10-pound bag, Doug's grass seed contains 11.0% more grass seed than the generic brand.
• In a typical 10-pound bag, the generic grass seed contains 13.3% less grass seed than Doug's brand.

Altering Data Sets: Consider the following data set:

2, 5, 7, 7, 9, 12

Without calculating the statistics, describe what would happen in each case.

(a) The 12 is replaced by a 24.

• The mean would increase.
• The median would stay the same.
• The standard deviation would increase.
• All of these are true.

(b) The 2 becomes a 0 and the 12 becomes a 14.

• The standard deviation would increase.
• The median would increase.
• The mean would increase.
• All of these are true.

(c) One of the 7's is replaced by a 14.

• The mode would disappear.
• The mean would change.
• The median would change.
• All of these are true.

Simpson's Paradox, Wage Discrepancy: Here is a fictitious example where an average across categories conflicts with the averages obtained within categories. This is called Simpson's Paradox.

Suppose you own a contracting company and employ 16 people (8 males and 8 females). Your employees are paid on an hourly basis and the wages (in dollars per hour) are given in the table below. You are accused of discriminatory pay practices because the average wage for the males ($33.25 per hour) is greater than the average wage for the females ($28.75 per hour).

Gender	less than 5 years of experience	more than 5 years of experience	average (mean)
Male	23, 27	34, 34, 36, 36, 38, 38	33.25
Female	22, 24, 27, 27, 28, 28	35, 39	28.75

(a) Within the category of less than 5 years of experience, calculate the average hourly rate for the males and the females. Round your answer to 2 decimal places.

For males with less than 5 years of experience:

For females with less than 5 years of experience:

(b) Within the category of more than 5 years of experience, calculate the average hourly rate for the males and the females. Round your answer to 2 decimal places.

For males with more than 5 years of experience:

For females with more than 5 years of experience:

(c) Within each category, who has the higher average?

• females
• males

(d) What caused the discrepancy between the over-all male/female averages and those found within each category?

• Workers with more than 5 years of experience get paid more.
• There were more males with over 5 years of experience.
• There were not many females with more than 5 years of experience.
• All of these contributed to the discrepancy.

Altering Data Sets: Consider the following data set:

26, 31, 34, 35, 38, 42

Without calculating the statistics, describe what would happen in each case.

(a) The 26 is replaced by a 13.

• The mean would decrease.
• The median would stay the same.
• The standard deviation would increase.
• All of these are true.

(b) The 26 becomes a 22 and the 42 becomes a 46.

• The median would increase.
• The standard deviation would increase.
• The mean would increase.
• All of these are true.

(c) The 35 becomes a 42.

• The mean would increase.
• The mode would now be 42.
• The median would change.
• All of these are true.

Sample Statistics: Calculate the requested statistics for the following sample data:

5.7, 3.8, 5.3, 3.8, 4.8

Give the answer to the proper number of decimal places outlined below.

If you get a message that says, "Check the number of significant figures", that means you essentially have the correct answer but the wrong number of decimal places.

(a) mean =

(b) median =

(c) mode =

(d) range =

(e) variance =

(f) standard deviation =

Rounding Rules:

• Mean, Standard Deviation, and Variance: Your answer should be rounded to one more decimal place than the raw data.
• Median: If you have to take the mean of two numbers then round that result to one more decimal place than the raw data. If one of the elements of the data set is the median, then use that number as is.
• Intermediate Steps: When performing intermediate steps to do something like calculate the standard deviation, it is best to round to at least one extra decimal place than will be used in the final answer.

Simpson's Paradox, Wage Discrepancy: Here is fictitious example where an average across categories conflicts with the averages obtained within categories. This is called Simpson's Paradox.

The manager at the GARP clothing branch in the mall is applauded for treating male and female sales representatives equally with respect to pay. This is demonstrated by the averages given in the table below. The average (mean) of the 6 males is $17.00/hour which equals the average for the 7 females. We will look at the data but refine our focus to include average pay within the categories of assistant and associate sales positions.

Gender	Assistant Sales representatives	Associate Sales representatives	average (mean)
Male	15, 15, 16, 17	19, 20	17.00
Female	14, 15	16, 17, 18, 19, 20	17.00

(a) Within the category of Assistant Sales Representatives calculate the average hourly rate for the males and the females. Round your answer to 2 decimal places.

Average wage for male assistant sales reps:

Average wage for female assistant sales reps:

(b) Within the category of Associate Sales Representatives calculate the average hourly rate for the males and the females. Round your answer to 2 decimal places.

Average wage for male associate sales reps:

Average wage for female associate sales reps:

(c) Within each category, who has the higher average wage?

• females
• males

(d) How did the pay differences between males and females within each category get hidden in the over-all averages?

• Associate sales representatives get paid more (on average).
• There were fewer male associate sales representatives.
• There were more female associate sales representatives.
• All of these contributed to the pay differences being hidden in the over-all averages.

Quarterbacks: Assume heights and weights are normally distributed with the given means and standard deviations from the table below.

Strata	Mean Height (inches)	Standard Deviation Height (inches)	Mean Weight (pounds)	Standard Deviation Weight (pounds)
U.S. Men	69.3	2.8	191	28
U.S. Women	64.0	2.8	145	32
NFL Quarterbacks	76.5	1.8	245	25
Top Female Models	70.0	2.2	115	18

Tom Brady is a quarterback in the NFL. He is 76 inches tall and weighs 225 pounds. Round your z-scores to 2 decimal places.

(a) With respect to all U.S. men, the z-score for his height is.

(b) With respect to all U.S. men, the z-score for his weight is.

(c) With respect to all U.S. men, would his height be considered unusual?

• Yes
• No

(d) With respect to all U.S. men, would his weight be considered unusual?

• Yes
• No

AM -vs- PM Test Scores: In my PM section of statistics there are 30 students. The scores of Test 1 are given in the table below. The results are ordered lowest to highest to aid in answering the following questions.

index	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
score	45	48	50	52	55	60	61	63	64	65	66	67	68	71	75
index	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
score	77	80	80	81	82	85	87	89	90	92	92	93	94	99	100

(a) The value of P₉₀ is.

(b) Complete the 5-number summary.

Minimum =

Q₁ =

Q₂ =

Q₃ =

Maximum =

Simpson's Paradox, Derek -vs- David: Averaging across categories can be misleading but this can be resolved with weighted averages.

In baseball, the batting average is defined as the number of hits divided by the number of times at bat. Below is a table for the batting average for two different players for two different years.

The number in parentheses gives the number of times at bat for each player for each year.

	Batting Average (# of times at bat)
	1995	1996
Derek	0.251 (55 times at bat)	0.313 (585 times at bat)
David	0.254 (405 times at bat)	0.322 (145 times at bat)

(a) What are the averages of the two batting averages for Derek (x_Derek) and David (x_David)?

Do NOT use a weighted average, just take the mean of 1995 and 1996 batting averages. Round your answers to 3 decimal places.

(b) Who had the higher average batting average using the non-weighted average?

• Derek
• David

(c) Using a weighted average, calculate the average batting averages for Derek (x_Derek) and David (x_David). Round your answers to 3 decimal places.

(d) Who had the higher average batting average using the weighted average?

• Derek
• David

(e) What caused the discrepancy in average batting averages?

• Derek's higher average occurred with more times at bat (585).
• David's higher average occurred with fewer times at bat (145).
• Derek's lower batting average was based on a small number of times at bat (55).
• All of these contributed to the discrepancy.

Attachment:- Assignment File.rar