Question

8) As part of a study of corporate employees, the Director of Human Resources for QRS Company wants to compare the distance traveled to work by employees at their office in downtown Cincinnati with the distance for those in downtown Pittsburgh. a) State the Hypothesis to show mean number of miles traveled per month is different for Cincinnati and Pittsburgh employees. b) Choose a level of a. Use a = 0.05 for this problem. c) To test the hypothesis, the researcher collects data on 35 workers in the Cincinnati office and 40 in the Pittsburg office. The data appear in the QRS Company worksheet of the HW1 data workbook on Moodle. Collect data and calculate necessary statistics to test the hypothesis. d) Sketch the sampling distribution. Include the critical value and test statistic e) Draw a conclusion and report that in the problem context. f) Calculate the p-value for the hypothesis test g) Use Excel to perform the hypothesis test.

Cincinnati	Pittsburg
406	347
333	379
346	360
331	360
400	379
368	339
350	385
384	353
351	397
369	369
368	418
362	367
334	391
313	387
322	421
335	370
412	353
317	353
378	376
415	382
376	410
434	371
388	402
408	402
377	354
371	391
382	412
367	305
365	385
363	412
410	346
367	411
374	401
407	393
367	360
	366
	409
	389
	372
	423

Answer 1

a) NULL HYPOTHESIS H0: $\mu (C)= \mu (P)$

ALTERNATIVE HYPOTHESIS Ha: $\mu (C)\ne \mu (P)$

b) Level of Significance (alpha)= 0.05

c) To test the hypothesis we will assume following assumptions:

i) The samples are independent to each other.

ii) The samples are normally distributed.

iii) Populations Variances are unknown and equal to each other.

To verify last assumption we will use F test .

H0: POPULATION VARIANCES ARE EQUAL

Ha: POPULATION VARIANCES ARE NOT EQUAL.

From above test we can see that P value=0.1936 >0.05 therefore NOT SIGNIFICANT.

We can conclude that population variances are equal.

Now

From above table we can see that

t stat= -1.546

t stat= 1.546 (Two tailed test)

t critical= 1.99

P value =0.1263

Since P value >0.05 level of significance therefore NOT significant.

Decision: Fail to reject H0.

Conclusion: We don't have enough evidence to conclude that mean number of miles traveled per month is different for Cincinnati and Pittsburgh employees.