Question

Listed below are measured fuel consumption amounts (in miles per gallon) for a random sample of cars. Acura RI Acura TSX Audi A6 BMW 525i City Fuel Consumption 18 22 21 Highway Fuel Consumption 26 31 We are going to do a matched pairs test to see if there is sufficient evidence at the 5% significance level to support the claim that there is a difference in city and highway fuel consumption. a. Define the parameter and state the hypotheses. [4 pts] 21 29 28 b. Find the observed sample statistic and the test statistic. Use proper notation for the sample statistic (or ), and clearly identify your test statistic as either a z-score or a t-score. [4pts] c. Find the p-value of your test statistic. You are required to graph the test statistic on its corresponding distribution, shade the appropriate area, and provide correct calculator documentation. Box final answer. [3pts] d. Make a generic decision about H - [2pts] e. Make a conclusion in the context of the problem. [2pts] f. Do you have any concerns with this hypothesis test? clearly answer "yes" or "no". — Explain your answer.

Answer 1

I let the data as below, 2) Acura RI Acura TSX Audi A6 BM LO 5253 cily fuel 18 22 21 Consumphon Highway Fuel 3) 28 consumphon 29 a) paramelers ni = n2 = 4 Ex = 18+ 22+ 21+21= 82 Exer= 26 +31 +29+28=114. 9 = 13 3 XL = 20.5 X2=28.5. S, ECXI - X,)? Si=3 not 32² E(X2-X2)² 2) 52 = 4.83 Testing the null & alternative hypothesis a Hoi el=12 i.e. There is no difference bem cily heel consum pHon f Highway fuel consumpHon. V Hi M742 i.e. There is difference beth at hiel consumphon f Highway Reel consumptes

n=4 b) If sample size Use the t-test The test statistic + Xi X2 S2 S23 + n2 20.5- 28.5 4.33 + Le 4 1.3540 .:Itscone = -5.9084 It=5,9084 p-value = P(Z > -5,9084) = 0.0010 <0.05 at &=0.05 & df = nith2-2=6. P-value = 0.0010 p-ratue a 0.0005 p-value=0.0005 t=-5.9084 t=5.9084

d) Decision & Reject the null hypothesis e conclusions we condude that the There is a difference in city 4 highway fuel consumption f) No.