Crash tests at 5 miles per hour were performed on five randomly selected small pickups and eight randomly selected small utility vehicles. For the small pickups, the mean bumper repair cost was $1090 and the standard deviation was $403. For the small utility vehicles, the mean bumper repair cost was $485 and the standard deviation was $382. At =0.10, can you conclude the the mean bumper repair cost is greater for small pickups than for small utility vehicles? Assume the population variances are equal. State the null and alternate hypotheses and calculate the value of the test statistic. Determine the critical value and the rejection regions and make a decision and interpret it.
Explanation / Answer
Xbar1=1090; s1=403; n1=5 Xbar2=485; s2=382; n2=8 =.1 / Ho:1-2=0 H1:1-2>0 Since we can assume the population variances are equal thetest statistic is t=(Xbar1-Xbar2)/[Sp(1/n1+1/n2)] whereSp=[(n1-1)s12+(n2-1)s22]/ and =n1+n2-2 which is the degrees of freedom of t. For the values above: =11 Sp=151919 t=.006986 Critical value is t.1=1.36 Hence we cannot reject Ho.