Tests for 2-sample Data

Use the following data set on rates of reported rapes for 72 metropolitan areas selected from the North and the West (from: Department of Justice, Uniform Crime Reports for the U.S.)


        North                   Rate            West            Rate

        Akron,OH                39              Bakersfield,CA  58 
        Allentown,PA            18              Brownsville,TX  18 
        Ann Arbor,MI            87              Colorado Sp,CO  69 
        Atlantic City,NJ        54              Denver,CO       47 
        Benton Harbor,MI       100              Fresno,CA       65 
        Boston,MA               32              Galveston,TX    46 
        ...                                     ... 
        Syracuse,NY             23              Victoria,TX     32 
        Vineland,NJ             55              Waco,TX         45

We want to investigate the research hypothesis that the mean rate of reported rapes is higher for the West.

Question 1: Formulate the null and alternative hypotheses.

Question 2: Perform a two-sample ttest at alpha=0.05. Report the P-value and state your decsion.

Again, Minitab will do all your work. First copy the dataset to your account (do this {\em before} you start Minitab):

 cp /afs/acpub/project/sta215/crime.data crime.data
 minitab
 read 'crime.data' c1 c2}
 name c1='NORTH' c2='WEST'
 twosample 'WEST' 'NORTH';
 alternative=1.

The output gives you the P-value for a test with null hypothesis H0: mu[west] = mu[north] versus H1: mu[west] > mu[north].

Confidence intervals

In the two sample t test of the previous example the printout from the command {\tt twosample} also included a confidence interval for the unknown mu[west]-mu[north].

To obtain a confidence interval for the unknown mean mu in the one-sample data problem of Case Study 9.2. use the command interval. If you have left Minitab since going through the example in Section 3, you need to first repeat entering the data. Then type:

	tinterval 95 'SLEEP'

to obtain a 95% confidence interval for the unknown mu.

Question: State the 95\% confidence interval for mu.