Statistics - Assignment Example

due Statistics Assignment Question Summary Statistics Life Expectancy Mean 76.0752 Standard Error 0.257757 Median 76.38245Mode#N/AStandard Deviation1.840753Sample Variance3.388371Kurtosis-0.55827Skewness-0.66657Range6.808189Minimum71.86361Maximum78.6718Sum3879.835Count51From 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 3African American Life ExpectancyMean71.

43484Standard Error0.398077Median71.07148Mode#N/AStandard Deviation2.321168Sample Variance5.38782Kurtosis0.069348Skewness0.478407Range10.50305Minimum66.53079Maximum77.03385Sum2428.785Count34Asian American Life ExpectancyMean85.16029Standard Error0.552585Median85.98477Mode#N/AStandard Deviation2.471233Sample Variance6.106993Kurtosis1.31323Skewness-1.09564Range9.582142Minimum78.49149Maximum88.07363Sum1703.206Count20LatinoMean80.57885Standard Error0.574033Median80.59902Mode#N/AStandard Deviation2.

567151Sample Variance6.590267Kurtosis-0.51856Skewness-0.2639Range9.760505Minimum75.54943Maximum85.30993Sum1611.577Count20Native American Mean71.4901Standard Error1.224867Median70.64433Mode#N/AStandard Deviation3.000299Sample Variance9.001795Kurtosis2.071864Skewness1.458784Range8.09211Minimum68.84757Maximum76.93968Sum428.9406Count6 White Mean76.46409Standard Error0.256491Median76.91389Mode#N/AStandard Deviation1.831714Sample Variance3.355177Kurtosis0.657977Skewness-0.05232Range9.423102Minimum72.

64288Maximum82.06598Sum3899.669Count51 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 5Contingency table T virus Machine Detection Right Wrong TotalHave 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 TotalHave 4.9%0.1%5%Have nots 90.254.75%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 7Given 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 defectiveP (not defective and damaged) = 10%* 99% = 9.9 %Expected loss from damage = 9.9% of $100 = $ 9.9Total 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 8Number of Customers entering the shop Mean0.52Standard Error0.031106Median0Mode0Standard Deviation0.76195Sample Variance0.580568Kurtosis5.327549Skewness1.897554Range5Minimum0Maximum5Sum312Count600 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 citedLind, Douglas A, William G. Marchal, and Robert D. Mason. Statistical Techniques in Business & Economics. Boston: McGraw-Hill, 2002. Print.