Practice Midterm 2 1. Suppose that you wish to compare two means ...

Practice Midterm 21. Suppose that you wish to compare two means for two populations andthat σ 2 1 =20andσ 2 2 = 30. What allocation of n =200sampleswillresultinthe maximum amount of information on the difference of the two populationmeans?2. The following table displays the number of goals scored by the SJ Sharksand the Chicago Blackhawks over the first 6 games of the season.Game 1 2 3 4 5 6Sharks 4 6 5 4 4 3Blackhawks 5 6 3 3 3 2a) Test at the 5% significance level to see if there is a difference in averagenumber of goals scored per game between the two teams. Clearly state yourconclusion.b) State all of the assumptions you used for part a).3. Refer to the data in exercise 13.13 on p 676.a) Test at the 5% significance level to see if there is a difference in meanmaneuver times for the three vehicle types. Clearly state your conclusion.b) State all of the assumptions you used for part a).4. The following link lists all worldwide earthquakes of magnitude 8 or moresince 1900:http://earthquake.usgs.gov/earthquakes/eqarchives/year/mag8/magnitude8 1900 date.phpConstruct a table for the number of years (to save time, since the year2000...or use all of the data if you are more ambitious) that have had n =0, 1, 2, 3, 4ormoremagnitude8(orhigher)earthquakesinthatyear. Then

use a chi square test to determine whether the data follows a Poisson distribution.Clearly state your conclusion.5. Suppose you have observations (x i ,y i )fori =1,...,n and you want torun a linear regression where y is the target variable and x is the predictorvariable.a) Write down the linear model equation for y i in terms of x i and explainthe assumptions about each term.b) Now consider the case of multiple linear regression where x i is nowa vector. The R function “summary” returns information on a fitted linearmodel, in particular the p-values of the estimated coefficients. What is themeaning of these p-values and how can they be used to improve the model?