MAT 382Homework for one mean

started on: Wednesday, 9Sept 2015

to be submittedon: Friday, 11Sept2015

Current Sections

  • Review your class notes.
  • The following questions are based on the data found in the spreadsheet
  • Please complete these requests for the traffic data:
  • First assess any assumptions you need for parts B&C (below).
  • Test whether the mean % change among 55mph states (e.g. Alaska) is different than 0 (no change). Use a significance level of =0.10.
  • Then construct a 90% level confidence interval for the mean from part B which is appropriate to your Ha from part B.
  • Explain how your test conclusion from part B and confidence interval from part C are consistent.

Please do either E-H below ORZ below.

  1. Now assess any assumptions you need for parts F&G (below).
  2. Test whether the mean % change among non-55mph states (e.g. Alabama) is more than 0. Use a significance level of =0.10.
  3. Then construct a 90% level confidence interval for the mean from part F which is appropriate to your Ha from part F.
  4. Explain how your test conclusion from part Fand confidence interval from part Gare consistent.

Z. [glimpse of the foundations of T-distributions]

  1. Look up the “representational definition” of T-distributions and write that definition. Caution: this definition is NOT in terms of the pdf of a T-distribution.
  2. Does the T-statistic from the blue sheet have a T-distribution? The correct answer is “yes if…”. Explain what should follow the “if” and why, under that condition, the T-statistic really does satisfy the definition in #1 above.
  3. Look up the pdf of T-distributions and graph the follow pdf’s overlaid in a single sketch: the pdf of a T-distribution with 1 degree of freedom

the pdf of a T-distribution with 5 df

the pdf of a T-distribution with 25 df

the pdf of a standard normal distribution

Comment on the shapes of each pdf and how the 4 pdf’s compare.

  • Please do and submit the following problem as a team:
  • HOMEGROWN, done in teams: Use the same gospel you investigated in the last assignment to estimate your gospel’s mean number of words per verse. Please use the New International Version if you can readily find one; if not, make clear which version you used. If you saved a list of the verses from your first homework, you may re-use them; if not, take a new random sample of 25 verses.

Use a 95% confidence interval to estimate your mean # words.

Be sure to check your method’s assumptions before using the method.

Complete as of 7 November 2018