40% of college students go to at least one concert on a weekday each year.

by | Jun 20, 2019 | Main

Historically, it is known that 40% of college students go to at least one concert on a weekday each
year. Avery and Aubriella believe that college students are in fact choosing to go to concerts on a weekday
less often. To explore their claim, they survey 60 students at their college. Of these 60 students, only 21 have
gone to a concert on a weeknight in the past year.

  1. What is Avery and Aubriella’s research question?
  2. What would be their observational unit?
  3. What is their variable? Is it categorical or quantitative?
  4. In words, what is the parameter of interest? What symbol do we use for this parameter?
  5. In symbols, what are our hypotheses? (Hint: Historical information implies this is information collected
    over a long-term.)
  6. What is their sample statistic? What symbol do we use for this?
  7. For Aubriella and Avery’s study, create a simulation to real-study table as we have seen in class.
  8. Go to www.rossmanchance.com/ISIapplets.html and click the One Proportion applet. Enter the
    appropriate numbers into the “Probability of heads” and “Number of tosses” boxes. Enter “1” for
    the number of samples, and press “Draw Samples.” Report the number of successes. What does this
    number represent?
  9. Select “Proportion of Successes.” Write down this proportion. How did the applet get this number?
  10. Change the number of samples from 1 to 99 and click “Draw Samples” again. This gives us a resulting
    100 samples.
    a. Comment on the shape of the resulting dot plot.
    b. Where is the plot centered? Why does this make sense?
    c. What does each dot on the plot represent?
  11. We can calculate the p-value by hand. How can we do that?
  12. Perform what you described in problem 12. What is the resulting p-value?
  13. Typically 100 repetitions do not provide a very good idea of the p-value. Why not? What should we do
    instead?
  14. Implement what you stated we should do instead in problem 14 in the applet. Use the applet to find
    your p-value. (Enter the observed statistic in the text box next to “Count”, make sure the inequality
    symbol matches the alternative hypothesis, and click “Count”.)
    a. What value did you get?
    b. Is this close to what you found by hand in question 13?
  15. Using our guidelines for the strength of evidence with p-values, what can Avery and Aubriella conclude
    based on the p-value found in problem 15? Remember a conclusion must be made in context.
  16. Was their observed sample statistically significant? Explain.
    2
  17. What is one way in which the strength of evidence Avery and Aubriella observed would increase?
    Explain.
  18. What is one way in which the strength of evidence Avery and Aubriella observed would decrease?
    Explain. It can not be the opposite of what you state in problem 18!
  19. Is the validity condition for the Theory-based Approach met for this situation? Why?
  20. Using the Theory-based Approach, what is the standard deviation? (Show all work for credit.)
  21. Using the result from question 21, what is our standardized statistic? (Show all work for credit.)
  22. Using our guidelines for the strength of evidence with standardized statistics, what can Avery and
    Aubriella conclude based on the standardized statistic found in problem 22? Remember a conclusion
    must be made in context.
  23. Verify your answer in problem 22 with an appropriate applet.
    a. What applet did you use?
    b. What was the p-value?
    c. What was the standardized statistic?
  24. Are the p-values in problem 15 and problem 24 similar? Explain why or why not.

Sample Solution

This question has been answered.

Get Answer