Question

Maintence (Diesel Engine)	Maintence (Gas Eng)
503	514
380	466
432	359
329	427
503	474
505	382
546	474
561	558
357	497
329	459
489	355
455	436
503	514
380	406
432	474
478	382
471	422
444	474
493	558
452	360
461	460
496	423
469	477
433	453
561	444
357	457
329	461
525	455
374	462
389	470
450
561
581
427
366
382
370
400
527

   

(1) Using the informatin above, Carry out a “t-test: Two-Sample Assuming Unequal Variances” in Excel (with ? = 0.05) that tests whether there is a difference in mean maintenance costs between buses with Diesel engines and those with gasoline engines. Show all the steps.

(2) Based on the t-test, what is your decision (“reject” or “do not reject”) regarding the null hypothesis that the two population means are equal to each other? Indicate on which part of the Excel output you base your decision.

(3) Explain what the decision in part (b), i.e., “rejecting H₀” or “not rejecting H₀” means in this context at a level that can be understood by a high school senior.

     

            

Answer 1

(1)

Steps in Excel :

1. Enter the data, then go ot Data and select Data analysis from there.

2. Now select "t-test: Two-Sample Assuming Unequal Variances".

3. Enter the input range for both the variables and set alpha =0.05.

4. Set Hypothesized Mean Difference = 0 and click OK.

Output will be generated as :

Null hypothesis Ho : There is no difference in mean maintenance costs between buses with Diesel engines and those with gasoline engines.

Alternative hypothesis H1 : There is a difference in mean maintenance costs between buses with Diesel engines and those with gasoline engines.

Decision criteria : If P-value < alpha( level of significance) we reject Ho.

(2) In the excel output we consider the value P(T<=t) = 0.837953 on which we base our decision.

Now since P-value = .837953 > 0.05 (level of significance) we do not reject Ho and conclude that There is no difference in mean maintenance costs between buses with Diesel engines and those with gasoline engines.

(3) Decision in the part (2) was to not reject Ho and conclude in context at a level that can be understood by a high school senior that There is no difference in mean maintenance costs between buses with Diesel engines and those with gasoline engines.