Mathematics

Chapter 8

  1. Global Warming  In April 2011, a Yale/George Mason poll of 1010 US adults found that 40% of the people responding believed that scientists disagreed about whether global warming exists.  They reported a 95% confidence interval of 37% to 43%.
    1. What was the study’s margin of error?
    2. If the researchers  wanted to be 98% confident, would their confidence interval be wider or narrower?
    3. If the researcher wanted to reduce the margin of error, would they need to make their level of confidence higher or lower?
    4. If the researchers had polled more people, would the interval’s margin of error have been larger or smaller?
  2. MLB  In a sample of 30 current MLB pitchers, the mean age was 28 years with a standard deviation of 4.4 years.  Using StatCrunch, construct a 95% confidence interval to estimate the mean age of all current MLB pitchers.
    1. Give the interval, round values to 1 decimal place:___________________
    2. State the correct numerical values that would be in each of these numbered spots in this diagram of this confidence interval.

  3. Contributions Please  The Paralyzed Veterans of America is a philanthropic organization that relies on contributions.  They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution.  To test a new campaign, they recently sent letters to a random sample of 100,000 potential donors on their mailing list and received 4781 donations.
    1. State the 95% confidence interval in correct conclusion sentence form for the true proportion of their entire mailing list who may donate.  Round values 3 decimal places.
    2. A staff member thinks that the true rate is 5.5%.  Given the confidence interval you found, do you find the staff member’s percentage plausible?  Explain why or why not.

 

Chapter 9

 

  1. Living with Parents   Many young adults live at home with their parents due to various reasons, such as lack of income, postponing marriage, and saving money for school.  A recent survey reports that approximately 36% of all young adults (ages 18-31) live with their parents (Fry, 2013).  In order to check this claim, a random sample of 440 young adults was obtained and 183 of them were found to live with their parents. Is there sufficient evidence to conclude that the proportion of young adults who live at home with their parents is higher than the value the survey reported?  Use α = 0.01.
    1. What was the data that was collected in this problem?
    2. Is this quantitative data or qualitative data?
    3. State the value of the sample statistic rounded to 2 decimal places.
    4. State the value of the population parameter that is being tested in this problem.
    5. State the level of significance given in the problem.
    6. State the hypotheses using the correct statistical symbols.
    7. State the test statistic rounded to 2 decimal places.
    8. State the P-value rounded to 4 decimal places.
    9. What is the correct decision?
    10. In a complete sentence, indicate the strength of this P-value and give a conclusion using the SPECIFIC context of the problem that you are testing.  I should be able to read this conclusion sentence and know specifically what the test was about.

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