Exam III

1. If you take a sample from a certain population of people that has a mean height of 67 inches, is it likely that the average height of people in the sample will also be 67 inches? If the standard deviation of the population is 2 inches, and you took a large number of samples consisting of 100 individuals, in what range of values would you expect 95% of the sample averages fall?
2. The February 24, 2006 edition of The Daily Sentinel reported that of 335 visitors questioned as part of a survey done by the McDowell Group, 78 percent were "very satisfied" with their time in Sitka.
   1. Compute the margin of error for the percent of individuals who were "very satisfied" with their time in Sitka.
   2. The reported margin of error was 5.5 percent. Does this agree with your calculation? Does it appear that the 'rule for sample proportions was used' to calculate the margin of error or the formula using the sample proportions?
   3. Construct a 95% confidence interval for the true proportion of visitors to Sitka who are "very satisfied" with their visit.
   4. Assuming the sample is representative of all multiday visitors to Sitka, can you reasonably conclude that more than 50% of all such visitors are "very satisfied" with their visit? Can you reasonably conclude that more than 75% of all such visitors are "very satisfied" with their visit? Explain.
   5. In the March 22, 2006 edition of The Daily Sentinel, Victor R. Scarano refers to the McDowll group study and writes,

      		The confidence level of the statistical sampling of travelers
      		was 95 percent and yielded some key findings.  In essence, a
      		95 percent confidence level in the sampling means, if every air
      		visitor was questioned, they would answer in line with the 
      		sample group 95 percent of the time.
      	    

      Explain what you think the statement is saying. Is this a correct interpretation of a statistical confidence level?
3. Suppose a food manufacturer is testing two different processes for making a certain product. They are comparing the current process with a new, cheaper, process and want to know if customers can tell any difference in taste. Give null and alternative hypothesis that a researcher investigating this situation would use. Describe the possible errors (Type I and Type II) that can occur and indicate the likely result of each error. Explain which, if either, of the errors is the worse one to make.
4. What is the difference between the word 'significance' in a statistical context and in more typical common usage context? Use examples to help explain your answer.
5. Consider a study with 30 subjects who are told they will be involved in a study on the effects of caffiene and sleep. They are randomly chosen to be given a caffiene pill or a placebo. The report of the study claims that caffiene has no effect on the amount of sleep a person is able to get. Do you think this conclusion is likely to be justified based on the study as described? Explain why or why not. (Assume all aspects of the study were conducted properly.)
6. Why is it useful to combine multiple studies about the same question? Describe two ways this can be done and give an advantage and disadvantage for each.