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Statistics - Assignment Example

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Summary
The scatter diagram shows that higher income earners have higher life expectancy. Note also that the scatter is denser below 35,000.
From the charts above, it’s precisely evident that high school…
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due Statistics Assignment Question Summary Statistics Life Expectancy Mean 76.0752 Standard Error 0.257757 Median 76.38245
Mode
#N/A
Standard Deviation
1.840753
Sample Variance
3.388371
Kurtosis
-0.55827
Skewness
-0.66657
Range
6.808189
Minimum
71.86361
Maximum
78.6718
Sum
3879.835
Count
51
From the summary statistics, the data is normally distributed with the mean approximately equal the median. (76.0752 ≈ 76.38245). Moreover, the skewness is not statistically different from zero.
Question 2
Life expected can be termed as directly influenced by the average income. The scatter diagram shows that higher income earners have higher life expectancy. Note also that the scatter is denser below 35,000.
As the number of individuals with less than high school education drops below 15, life expectancy rises above average.
From the charts above, it’s precisely evident that high school education is a better indicator of life expectancy. The effect of income is not clear, given that higher income does not guarantee higher life expectancy and vice versa.
Question 3
African American Life Expectancy
Mean
71.43484
Standard Error
0.398077
Median
71.07148
Mode
#N/A
Standard Deviation
2.321168
Sample Variance
5.38782
Kurtosis
0.069348
Skewness
0.478407
Range
10.50305
Minimum
66.53079
Maximum
77.03385
Sum
2428.785
Count
34
Asian American Life Expectancy
Mean
85.16029
Standard Error
0.552585
Median
85.98477
Mode
#N/A
Standard Deviation
2.471233
Sample Variance
6.106993
Kurtosis
1.31323
Skewness
-1.09564
Range
9.582142
Minimum
78.49149
Maximum
88.07363
Sum
1703.206
Count
20
Latino
Mean
80.57885
Standard Error
0.574033
Median
80.59902
Mode
#N/A
Standard Deviation
2.567151
Sample Variance
6.590267
Kurtosis
-0.51856
Skewness
-0.2639
Range
9.760505
Minimum
75.54943
Maximum
85.30993
Sum
1611.577
Count
20
Native American
Mean
71.4901
Standard Error
1.224867
Median
70.64433
Mode
#N/A
Standard Deviation
3.000299
Sample Variance
9.001795
Kurtosis
2.071864
Skewness
1.458784
Range
8.09211
Minimum
68.84757
Maximum
76.93968
Sum
428.9406
Count
6
White
Mean
76.46409
Standard Error
0.256491
Median
76.91389
Mode
#N/A
Standard Deviation
1.831714
Sample Variance
3.355177
Kurtosis
0.657977
Skewness
-0.05232
Range
9.423102
Minimum
72.64288
Maximum
82.06598
Sum
3899.669
Count
51
Normally distributed with a skewness not statistically different from zero. The total count of 51 implies that the whites dominate many states, given that the other races have a lesser counts.
Question 4
African American
Higher income does not result to high life expectancy.
Asian American
Life expectancy is generally high; income does not seem to influence life expectancy.
Latino
Latinos income is fairly lower than the other races; however, life expectancy is similar to the rest; evenly distributed among income levels.
Native American
An increase income increases life expectancy. This contradicting result might be attributed to the small sample size.
Whites
Higher life expectancy is evident in higher income earners. However, low income earners (below 40000) tend to be evenly distributed across all life expectancies.
In a nutshell, income slightly influences life expectancy, but might not be as a good predictor due to the results controversies. In theory, an increase in income increases life expectancy, but the data results show a high concentration of low income earners having high life expectancy across all other races.
Question 5
Contingency table
T virus
Machine Detection
Right
Wrong
Total
Have
4.95%
0.05%
5%
Have nots
85.55%
9.5%
95%
Total
90.45%
9.55%
100%
The totals in the last row represent the machines total effectiveness and can be used to refer to machines effective probabilities.
Question 6: Using the same information in problem 5,
The probability that an individual:
tests positive for the virus is actually infected is 4.95%
that tests negative for the virus is not infected is 85.55
Is this a reasonable test to have the general population take?
The machine is effective as it gives results at a confidence level of 90.45% but a more effective machine that allows for a significant level of 5% or 1% would be better.
If a new test was available that was 98% effective at successfully detecting the T Virus and only falsely detected the T Virus 5% of the time, The contingency table would thus be
T virus
Machine detection
Right
Wrong
Total
Have
4.9%
0.1%
5%
Have nots
90.25
4.75%
95%
Total
95.15%
4.855%
100%
And thus the probability that an individual tests positive for the virus actually has the virus would be 4.95 %
Question 7
Given the probability of the phone being detective (P (Def.) = 1%
The expected loss from defect + 1%*500 = $5
For the phone to get damaged it must be bought and used and thus not defective
P (not defective and damaged) = 10%* 99%
= 9.9 %
Expected loss from damage = 9.9% of $100
= $ 9.9
Total expected loss = $ (9.9 + 5) = $14.5
Since the expected loss is less than the warranty cost, then it is rational not to buy it. Buying the warranty would only become rational when its price is less than or equal to the expected loss ( i.e ≤ $14.5). With expected loss less than the price, taking the risk becomes more expensive than protection.
Question 8
Number of Customers entering the shop
Mean
0.52
Standard Error
0.031106
Median
0
Mode
0
Standard Deviation
0.76195
Sample Variance
0.580568
Kurtosis
5.327549
Skewness
1.897554
Range
5
Minimum
0
Maximum
5
Sum
312
Count
600
The expected number of customers per minute is less than 1, implying that the shop hardly gets clients. However, the data is positively skewed, implying that entrance is higher than the mean in most of the minutes.
The histogram resembles a poison distribution, with high frequency for smaller expected visitors which reduced as one moves on.
Work cited
Lind, Douglas A, William G. Marchal, and Robert D. Mason. Statistical Techniques in Business & Economics. Boston: McGraw-Hill, 2002. Print. Read More
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