Suppose I have data on federal funding for education for all 50 states (thepopulation).
The population mean = 25 (in millions of dollars) and the population standard
deviation = 6.
You draw a random sample of 10 states and get the following values for federal
funding (in millions of dollars):
17, 32, 22, 28, 31, 9, 15, 22, 18, 13
1. Calculate the mean, mode and median for the sample.
2. Calculate the sample standard deviation (s).
3. Calculate the standard deviation of the sample mean (also known as the
standard error of the sample mean) using the information on the
POPULATION.
4. Using what you found in part c, construct a 95% confidence interval for
the sample mean. Draw a graph of the interval and explain your finding.
What can you say about the population mean based on your confidence
interval?
5. Do the same as in part d, but use an 80% level of confidence.
6. Given the information on the POPULATION, what is the probability that a
randomly chosen state from the population will get funding in excess of
34.9 million dollars?
7. Given the information on the POPULATION, if your state received 23
million dollars in funding, what percentile would your state be in? i.e.
what percent of states would receive less than your state?
8. Suppose a spokesperson from the federal government claims that the
population mean for federal funding is really 27 million. Given your
confidence intervals above, is this figure believable? Why or why not?
9. Suppose you do NOT know the population standard deviation, so you
have to use the sample standard deviation, s, from question #2 to
calculate the standard error of the mean. Construct a 95% confidence
interval for the sample mean. Draw a graph and explain your interval.
Based on your confidence interval, is your sample representative of the
population? How do you know?
10. Suppose the first 5 states are drawn from the North and the second 5
states are drawn from the South. Using ONLY the sample information,
conduct a difference in means test to determine whether there is a
difference in average funding given to northern versus southern states.
Explain what you find. Based on the sample and your results, did the
federal government discriminate in its distribution of education
funding?
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