 # Mathematics - Statistics Questions

Subject Mathematics Statistics-R Programming

## Question

7.1.2
According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft.In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the random variable, population parameter, and hypotheses.7.1.6
7.2.4
According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft.In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? Test at the 5% level.
7.2.6
In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and developmental," 2008). Nationally 1 in 88 children are diagnosed with ASD ("CDC features -," 2013). Is there sufficient data to show that the incident of ASD is more in Arizona than nationally? Test at the 1% level.
7.3.6
The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #7.3.8 ("SOCR data 2008," 2013). Countries that are considered high-income have a mean economic dynamism of 60.29. Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Test at the 5% level.

Table #7.3.8: Economic Dynamism of Middle Income Countries
25.8057
37.4511
51.915
43.6952
47.8506
43.7178
58.0767
41.1648
38.0793
37.7251
39.6553
42.0265
48.6159
43.8555
49.1361
61.9281
41.9543
44.9346
46.0521
48.3652
43.6252
50.9866
59.1724
39.6282
33.6074
21.6643

7.3.8
Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in table #7.3.10 ("Maintaining balance while," 2013). Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level.

Table #7.3.10: Forward/backward Sway (in mm) of Elderly Subjects
19
30
20
19
29
25
21
24
50

8.1.4
Suppose you compute a confidence interval with a sample size of 100. What will happen to the confidence interval if the sample size decreases to 80?
8.1.8
In 2013, Gallup conducted a poll and found a 95% confidence interval of the proportion of Americans who believe it is the government’s responsibility for health care. Give the statistical interpretation.

8.2.6
In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and developmental," 2008). Find the proportion of ASD in Arizona with a confidence level of 99%.

8.3.6
The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #8.3.9 ("SOCR data 2008," 2013). Compute a 95% confidence interval for the mean economic dynamism of middle-income countries.
Table #8.3.9: Economic Dynamism (\$) of Middle Income Countries
25.8057
37.4511
51.915
43.6952
47.8506
43.7178
58.0767
41.1648
38.0793
37.7251
39.6553
42.0265
48.6159
43.8555
49.1361
61.9281
41.9543
44.9346
46.0521
48.3652
43.6252
50.9866
59.1724
39.6282
33.6074
21.6643

1. (Low-density lipoprotein (LDL) is an important part of blood cholesterol test. LDL higher than 130mg/dl is a risk factor of developing cardiovascular disease. To prevent cardiovascular disease, a health center had a free blood cholesterol test for all the people older than 65 in the community. A total of eight people attended the blood screening and their blood test results are listed below:
LDL(mg/dl): 130,143,114,110,123,110,134,124
a) (3pts) After the blood test, the nurse wants to know the mean LDL score
b) (3pts) After the blood test, the nurse wants to know the median LDL score
c) (3pts) After the blood test, the nurse wants to know the mode of LDL scores
d) (3pts) After the blood test, the nurse wants to know the range of LDL scores
e) (4pts) After the blood test, the nurse wants to know the variance of LDL scores
f) (4pts) After the blood test, the nurse wants to know the standard deviation of LDL scores
g) (4pts) After the blood test, the nurse wants to know the minimum LDL score
h) (4pts) After the blood test, the nurse wants to know the maximum LDL score
i) (4pts) After the blood test, the nurse wants to know the Interquartile Range of LDL scores

2. (1pt) Which of the following are measures of central tendency? Select all that apply
a. mean
b. median
c. mode
d. Variance
e. standard deviation
f. linear transformation

3. (1pt) Which of the following are measures of variability? Select all that apply
a. mean
b. median
c. mode
d. variance
e. standard deviation
f. linear transformation

4. In the 2013 Jerry’s Artarama art supplies catalog, there are 560 pages. Eight of the pages feature signature artists.
Suppose we randomly sample 100 pages. Let X = the number of pages that feature signature artists.
a. (3pts) What values does x take on?
b. (3pts) What is the probability distribution?
c. Find the following probabilities:
i. (4pts)the probability that two pages feature signature artists
ii. (4pts)the probability that at most six pages feature signature artists
iii. (4pts)the probability that more than three pages feature signature artists.
d. Using the formulas, calculate the (i) (2pts) mean and (ii) (2pts) standard deviation.

5. (1pts) If a distribution is left-skewed, its mean is usually___ its median
a. bigger than
b. smaller than
c. equal to
d. we can not know

6. (1pts) A right-skewed distribution is also called a __ distribution.
a. Positively-skewed
b. Negatively-skewed
c. Kurtosis
d. Normal

7. (5pts) There are 20 coupons rolled up and placed inside round plastic balls in a box. There are 3 different types of coupons: 10 of them can be redeemed for “free drinks”, 5 can be redeemed for “free desserts”, and 5 can be redeemed for “free entrees”. If you shake the box and then randomly select one coupon. What’s the probability that you will get a free entree coupon?

8. (5pts) Mary was tossing a coin. She tossed three times. What’s the probability that at the first toss she gets a head, the second toss she gets a tail at and the third time she get a tail?

9. (5pts) Alice tossed a six-sided die three times. What’s the probability that she gets ones on all three throws?

10. (5pts) In a university with 3650 students, the professor wanted to know the probability that at least two students shared the same birthday. The probability will be:

11. (5pts) If you throw a six sided die twice, what is the probability that you will get a one on the first throw or a two on the second throw (or both)?

12. (5pts) James was playing poker . The whole set of cards is comprised of four suits: hearts, diamonds, spades, and clubs. Each suit has thirteen cards. Therefore, the whole set has 52 cards. James shuffled the cards and randomly chose two cards from the total of 52 cards. What’s the probability that both of the cards are from heart suits?

13. (5pts) Nick got a bag full of colorful jelly beans. There were 40 of them: 10 were red, 4 were yellow, 5 were orange, and 11 were blue. After shaking the bag, he randomly selected two jelly beans from the bag. What’s the probability that the first one was yellow and the second one was red?

14. (5pts) Jason got a bag full of colorful jelly beans. There were 40 of them: 10 were red, 4 were yellow, 5 were orange, and 11 were blue. After shaking the bag, he randomly selected two jelly balls from the bag. What’s the probability that the first one was a yellow and the second one was also a yellow?

15. (2pts) For which activity could probabilities NOT be computed using a Binomial Distribution? (Select all that apply)
a. Flipping a coin a 100 times
b. Throwing a die one hundred times
c. Flipping a coin only 5 times
d. SAT scores earned by all the students in a city

## Solution Preview

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1. a) Mean LDL = sum of all LDL score of 8 people / 8
= (130+143+114+110+123+110+134+124)/8
= 123.5
b) If we arrange data into ascending order, we have
110 110 114 123 124 130 134 143
Since median is average of 4th and 5th term ( because no. Of sample size is even)
Thus median is (123+124)/2 = 123.5
c) Since 110 is repeated most times, therefore, mode is 110.
d)Range = max LDL - min LDL = 143- 110 = 33
e) Variance = sum((x - mean )^2/n-1)
= Sum((110-123.5)^2+( 110-123.5)^2+ (114-123.5)^2 + (123-123.5)^2 +( 124 -123.5)^2 + (130-123.5)^2 + (134-123.5)^2+( 143-123.5)^2/7
= 988/7 = 141.1429
f) Standard deviation = sqrt(variance)
= sqrt(588/7) = 11.88 approx
g) Since
110 110 114 123 124 130 134 143
Thus
Min LDL = 110
h) 110 110 114 123 124 130 134 143
Thus
Max LDL = 143
i) Range of LDL scores
110 110 114 123 124 130 134 143
Quartile 1 (8*0.25) = 2nd value = 110
Quartile 3 (8*0.75) = 6th value = 130
Interquartile range = Quartile 3 - Quartile 1 = 130-110= 20.
2. a. mean
b. median
c. mode
d. Variance
e. standard deviation
All red marked are a measure of central tendency.
3.d. variance
e. standard deviation
f. linear transformation...

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