The relevant sections in the text are given after each problem number.
Instructions: Do problems 1; 2; 3 or 4 (but not both); 5 or 6 (but not both); 7; 8; 9 or 10 (but not both) for a total of 7 problems. Use the problem numbers given below on your submission (preferably a single file or, if not possible, a small number of files).
All work must be clearly shown (when there are calculations) for credit. If you used a Free Web App or other software system, indicate so, its name and what the inputs were.
1) 7.1
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). The overall concern is to determine if these data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%. For this problem, just state the random variable, the sample size, the population parameter, and the hypotheses.
2) 7.1
As in Problem 1, 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. The overall concern is to determine if these data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23% For this situation, state the Type I and Type II errors, consequences of each error type, and an appropriate Significance Level (alpha) to use. Explain your answers.
3) 7.2
As in Problem 1, 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. Do these data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? Test at the 5% level.
4) 7.2
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 there are more incidents of ASD in Arizona than nationally? Test at the 1% level.
5) 7.3
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
6) 7.3
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
7) 8.1
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) 8.1
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.
9) 8.2
In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) (“Autism and developmental,” 2008 – same information as for Problem 4) above). Find the proportion of ASD in Arizona with a confidence level of 99%.
10) 8.3
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 – same information as for Problem 5) above). Compute a 95% confidence interval for the mean economic dynamism of these 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