Question

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Question 5 (10 points) Wilcoxon Signed-Rank Test for n»30. When you are performing a Wilcoxon signed-rank test and the sample size n is greater than 30, you can use the StandardNormal Table and the formula below to find the test statistic 24 In this problem, perform the Wilcoxon signed-rank test using the test statistic for n>30 A petroleum engineer wants to know whether a certain fuel additive improves a car's gas mileage. lo decide, the engineer records the gas mileages (in miles per gallon) of 33 randomly selected cars with and without the fuel additive. The table shows the results. At α-0.10, can the engineer conclude that the gas mileage is improved? Car Without additive 36.4 36.4 36.6 36.6 36.8 36.9 37.0 37.1 37.2 37.2 36.7 With additive 36.7 36.9 37.0 37.5 38.0 38. 38.4 38.7 38.8 38.9 36.3 1 2345 678910 11 Car Without additive 37.5 37.6 37.8 37.9 37.9 38.1 384 40.2 40.5 40.9 35.0 With additive 38.9 39.0 39.1 39.4 394 39.5 39.8 40.0 40.0 40.36.3 12 13 14 15 16 17 18 19 20 2 22 Car Without additive 32.7 33.6 34.2 35.1 35.2 35.3 35.5 35.9 36.0 36.37.2 With additive 32.8 34.2 34.7 34.9 34.9 35.3 35.9 36.4 36.6 36.6 38.3 23 24 25 2627 28 29 303132 32

Answer 1

Null hypothesis: That is, a certain fuel additive does not improve a car's gas mileage Alternative hypothesis: That is, a certain fuel additive improves a car's gas mi Rejection rule: If p-valuesa-0.10), then reject the null hypothesis Ho EXCEL (Mega Stat in Add-Ins) procedure: eson Sienedl Rank Test Step 3: In Group 2, enter the second values Al:A34. Step 4: Check the Correct for ties and Select the appropriate Alternative as greater than. Step 5: Click OK. EXCEL (Mega Stat in Add-Ins) output:

Wilcoxon Signed Rank Test variables: With additive Without additive 483.5 sum of positive ranks 44.5 sum of negative ranks 32 n 264.000 expected value 52.173 standard deviation 4.207 z corrected for ties 1.29E-05 p-value (one-tailed, upper) The p-value is 0. Conclusion: Use a significance level, α-0.10 Here, p-Value is 0, which is less than the value of α-0.10 That is, p-value(-0)-α(-0.10) Therefore, by the rejection rule, reject the null hvpothesis Ho Interpretation There is sufficient evidence at level ofsignificance α = 0.10 That is, a certain fuel additive improves a car's gas m