STAtistics / Mr. Hansen

Name: _______________________

3/11/2010

Battery bonus (Mr. Hansen’s use only): _____

 

Test Through Chapter 11 (,, and All z and t Tests)

 

For the first three questions, give answer in terms of H0 and/or Ha. Use your own words. Do not simply give “cookbook” answers that reveal little knowledge. For example, do not say “1 minus power” or “probability of Type II error” for #1, since those statements reveal very little.

 

1. Define  as a conditional probability, i.e., P(whatever | whatever). Add a few additional words of explanation so that it is clear that you know what you are talking about.

 

 

 

 

2. Define  as a conditional probability, i.e., P(whatever | whatever). Add a few additional words of explanation so that it is clear that you know what you are talking about.

 

 

 

 

3. Define statistical power as a conditional probability, i.e., P(whatever | whatever). Add a few additional words of explanation so that it is clear that you know what you are talking about.

 

 

 

 

4.   Note that  can also be thought of as a “cutoff” value for P-values. Explain what it means for a P-value to be
(a) less than


(b) greater than

 

 

      (c) What value of  has been historically used probably more often than any other?

 

5.   Explain why we never speak of “power” as a single fixed value for all possible values of the alternative parameter value. Include a sketch in your explanation.

 

6.   Use two sketches, plus a sentence or two of explanation, to show that if all other aspects of a one-tailed statistical test for a single population proportion remain constant, but sample size is increased, then both  and  will decrease. Be sure to label the tick marks for the p0 and pa values on your sketches.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7.   Suppose that The Saint Albans News polled an SRS of 150 STA community members in 1999 and asked them if they thought Mr. Hansen was overzealous about dress code enforcement. (The community, then as now, included about 570 students, approximately 1000 parents, and more than 100 faculty members.) Of those polled in 1999, 79 said yes, Mr. Hansen is overzealous. Suppose that in 2009 the poll was repeated, again with an SRS of 150 community members, and this time, only 70 said that they thought Mr. Hansen was overzealous.

 

(a)  Is a paired test appropriate for determining if the change from 1999 to 2009 is statistically significant? Why or why not?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b)  As a “button pusher” (no work or assumption checking required), determine whether there is evidence of a decline in the true proportion of STA community members who think Mr. Hansen is overzealous. State the value of your test statistic, the P-value, and a full conclusion in context.

 

 

 

 

 

 

 

 

 

 

 

 

8.   Suppose that an SRS of 44 STA Upper School students had a mean of 6.9 hours of sleep in 2008-09, and when a different SRS of 44 people are tracked in 2009-10, the sample mean has dropped to 6.7 hours. Standard deviations are 0.7 and 0.85 hours, respectively. Suppose that there were 315 students in the Upper School each academic year. Is there evidence of a change in the mean amount of sleep between the two academic years? Conduct a statistical test and show all required steps. There is a small bonus for including the optional step.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.   In #8, explain why a paired study would probably have produced better results.