statistics hw

Read the paper titled “A Case Study of a Graphical Misrepresentation Drawing the Wrong

Conclusions about the Measles, Mumps and Rubella Virus Vaccine” from the journal “Drug

Safety” (this paper is available on Blackboard). Explain, in your own words, what is misleading

about the graph from the original article in Lancet. Explain, again in your own words, the

features of the proper graphing technique that should have been used. You may need to look

up what a “Population Pyramid” is, since that’s not something we covered explicitly in class (it’s

just a particular type of side-by-side bar chart). There’s a good explanation of the technique in

the Wikipedia article “Population Pyramid.” Make sure to include a reference for any research

you do.

Assume the prevalence of autism in the general population is five percent (5 out of 100 children

have some form of autism) and the percent of children who receive the MMR vaccine is 98%

(98 out of 100). Assume that, at random, 10 percent of the children with autism are first

diagnosed with autism within six months AFTER having received a dose of the MMR vaccine.

This is not an unreasonable assumption since MMR vaccinations and early autism diagnosis

often occur around the same age.

Even if there is no connection whatsoever between MMR and autism, out of a population of

one million children, how many children will APPEAR to have developed autism as a result of

the MMR vaccine (defined as autism being first diagnosed with six months after an MMR dose)?

What does this say about random chance, large populations, anecdotal data, correlation and

causation?

Note: the file “Anecdotal Information” on Blackboard has a similar analysis as an example. Part 2 – Energy Consumption

For the rest of the project, you will need to look at the “Energy Consumption Data” available on

Blackboard. Perform the following analyses for this data.

1. Find the mean, median, standard deviation and coefficient of variation for each of the

continental regions. See Chapter 3 for these calculations.

2. Based upon your answers from number 1, discuss the similarities or differences in

energy consumption between the continents. I want to know what the numbers mean

in real terms. I don’t just want, “A is higher than B and C is higher than D”. What are

the numbers telling us about energy usage in various places and how the usage varies

within a continent and from continent to continent? Can you think of reasons why the

countries with high energy usage use so much? Can you think of reasons why countries

with low usage use so little? Can you think of reasons why the continents with high

energy usage use so much? Can you think of reasons why continents with low usage

use so little? Are the reasons the same as when comparing country to country? What

does the coefficient of variation tell us about how widely scattered the numbers are for

the various continents? Can you think of reasons why the different continents might

have more or less variation?

3. Within the European continent, would any countries be considered to be unusually low,

or unusually high in terms of their energy consumption? Justify your answer

statistically. That is, use the statistical definition of unusual and explain how it applies to

the countries in question, if any. Why do you think those particular countries have

unusually low or high energy usage? Note that the statistical definition of unusual is not

the same as an outlier (see Chapter 3).

4. Create a group distribution for the North America/Caribbean countries and another

group distribution for the Europe countries. From these distributions, create a

histogram for each. Determine if each appears to be a normal distribution. For your

distributions, be sure to have 8 or more classes in order to maximize the reader’s ability

to see the shape of the distribution. You may exclude any outliers from the histogram

or create open-ended classes at the low end or high end to collect the outliers.

Include the appropriate titles and labels on the histogram. You must insert the

histograms into your paper. You can use Microsoft Excel to create the histograms, then

copy and paste them into your paper or you can draw the histograms by hand (or on a

computer) then scan or photograph them and insert them or use some other method.

Neatness and readability count!

Note: when you create a histogram for a continent, you are only using the values for

energy consumption. The country names do NOT go into the histogram! If you think

the country names need to be in the histogram, you are doing it incorrectly.

5. Find the 95% Confidence Interval for mean energy consumption for your European

sample. Explain what this confidence interval is telling you. 6. Find the 95% Confidence Interval for mean energy consumption for your North

American/Caribbean sample. Explain what this confidence interval is telling you.

7. Based on the two Confidence Intervals you found in #5 and #6, would you say that it is

possible that the two continents’ average energy consumption is equal? Explain how

you came to your conclusion.

8. Using one of the hypothesis test methods we have studied in class (Chapter 8 or 9), test

the claim that the North American/Caribbean energy consumption mean is the same as

the Asian energy consumption mean. Use a significance level of 0.05. Use the

appropriate two independent sample t-test to test this hypothesis. Since there are

several different hypothesis tests to choose from, explain the statistical reason you

selected the test you did. Be sure to include the reason behind each of your decisions

and your conclusions. You may exclude outliers before doing the test.

9. If the worldwide mean energy consumption per capita is 3000 kw-hr, would the North

America/Caribbean countries as a group be considered to have significantly higher

energy consumption than the world average? Assume we do not know the standard

deviation of energy consumption per capita for the entire world (meaning you can’t use

the normal distribution in your calculation). Be sure to clearly explain what hypothesis

test you are conducting (Chapter 8 or 9), and how you have made your decision.