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 University of Maryland, University College - STAT 200 STAT 200: Introduction to Statistics Homework #5 Solutions    1)Stephen Stigler determined in 1977 that the speed of light is 299,710

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 University of Maryland, University College - STAT 200

STAT 200: Introduction to Statistics Homework #5 Solutions 
 
1)Stephen Stigler determined in 1977 that the speed of light is 299,710.5 km/sec. In 1882, Albert Michelson had collected measurements on the speed of light ("Student t-distribution," 2013). Is there evidence to show that Michelson’s data is different from Stigler’s value of the speed of light? 
 a.) State the random variable 
 
b.) State the population parameter 
 
c.) State the hypotheses 
 
 
 
2. 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).  Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%?   a.) State the type I error in this case, consequences of this error type for this situation, and the appropriate alpha level to use. 
 
 
 
b.) State the type II error in this case, consequences of this error type for this situation, and the appropriate alpha level to use. 
 
3. 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).  
Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%?  Why or why not?  Test at the 5% level. 
 
i.) State the random variable and the parameter in words. 

ii.) State the null and alternative hypotheses and the level of significance The hypotheses for this experiment are given by: 

iii.) State and check the assumptions for a hypothesis test 

iv.) Find the sample statistic, test statistic, and p-value The sample proportion is given by: 

v.) Conclusion 
 
vi.) Interpretation (do not skip this part!  This is the “so what” of the entire hypothesis test). 
 
4. 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 the incident of ASD is more in Arizona than nationally?  Why or why not?  Test at the 1% level.  
 
i.) State the random variable and the parameter in words. 
 
ii.) State the null and alternative hypotheses and the level of significance The hypotheses for this experiment are given by: 
  
   
 
iii.) State and check the assumptions for a hypothesis test 

      
iv.) Find the sample statistic, test statistic, and p-value The sample proportion is given by: x = 507 n = 32,601 
?   
 
 

v.) Conclusion 
 
vi.) Interpretation (do not skip this part!  This is the “so what” of the entire hypothesis test). 
 
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 1 ("SOCR data 2008," 2013). Countries that are considered high-income have a mean economic dynamism of 60.29.  
Does the data show that the mean economic dynamism of middle-income countries is less than the mean for high income countries? Why or why not? Test at the 5% level. 
 
25.8057     37.4511     51.9150     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             
Table 1: Economic Dynamism of Middle Income Countries 
 
i.) State the random variable and the parameter in words. 
 
ii.) State the null and alternative hypotheses and the level of significance 
      
      
iii.) State and check the assumptions for a hypothesis test 

 
iv.) Find the sample statistic, test statistic, and p-value Sample mean and standard deviation: 
 
v.) Conclusion 
 
vi.) Interpretation 
 
 
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).  
Does the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Why or why not? Test at the 1% level. 
 
19     30     20     19     29     25     21     24     50 
Table 2: Forward/backward Sway (in mm) of Elderly Subjects 
 
State the random variable and the parameter in words. x = forward and backward sway of an elderly person
 
ii.) State the null and alternative hypotheses and the level of significance 
      
 
iii.) State and check the assumptions for a hypothesis test 
iv.) Find the sample statistic, test statistic, and p-value Sample mean and standard deviation: 
 
 
 
v.) Conclusion 
 
 
vi.) Interpretation 
 
 
7. 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? 
 
 
In 2013, Gallup conducted a poll and found a 95% confidence interval of 
0.52 p 0.60, where p is the proportion of Americans who believe it is the government’s responsibility for health care. Give the statistical interpretation. 
 
 
In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and developmental," 2008). Find the proportion of ASD in Arizona with a confidence level of 99%. 
 
 
i.) State the random variable and the parameter in words. 
      
ii.) State and check the assumptions  
iv.) Find the sample statistic and confidence interval 
 
  
v.) Real World Interpretation: 
 
 
10. 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 1 ("SOCR data 2008," 2013).  NOTE: 
this is the same data set from question 5.   
Compute a 95% confidence interval for the mean economic dynamism of middle-income countries.