Data on household vehicle miles of travel (VMT) are compiled annually by the Federal HighwayAdministration. A researcher is interested in whether there is a difference in last year's mean VMT forMidwestern and southern households (_Mand_S). Independent random samples of 15 Midwestern householdsand 14 southern households provided the following data on last year's VMT, in thousands of miles:

Midwest : 16.2,12.9,17.3,14.6,18.6,10.8,11.2,16.6,16.6,24.4,20.3,20.9,9.6,15.1,18.3

South : 22.2,19.2,9.3,24.6,20.2,15.8,18.0,12.2,20.1,16.0,17.5,18.2,22.8,11.5

a. Graph the data as you see fit. Why did you choose the graph(s) you did and what do they tell you? Also calculate summary statistics relevant to the research question.

midwest<-c(16.2,12.9,17.3,14.6,18.6,10.8,

11.2,16.6,16.6,24.4,20.3,20.9,9.6,15.1,18.3)

south<-c(22.2,19.2,9.3,24.6,20.2,15.8,18.0,

12.2,20.1,16.0,17.5,18.2,22.8,11.5)

b.Perform a 10% significance level two sample t-test for the difference in meansassumingequal varianceto address the researcher's question. Justify why the assumptions of thetest are reasonably met or describe what assumptions we are assuming are met.

As part of this test, specify yourassumptionsandhypotheses, calculate yourtest statistic,p valueand make aconclusion in the contextof the question. Show all steps of thecomputation by hand and then check your computations using t.test().

c.A confidence interval for the true difference in means_{M S}assuming equal populationvariances is reported as: (-3.527, 0.609). Identify the point estimate, margin of error, standarderror, critical value, degrees of freedom, and confidence level used to construct it.

d. Compute the test statistic and p value for the hypotheses:

H₀:_{M S}= 0, H_A:_{M S}= 0

at the 10% levelnotassuming equal population variances. You can use t.test(), but makesure you understand how those values are computed. How does the difference in populationvariances assumptions change how we do the calculations in the two independent sample ttest we perform?