Question

The Table below shows data of two random samples of employee wages taken from two small business firms providing the same service. The issue to be evaluated is whether the average wage in these two firms is the same. Test this hypothesis at α = 0.05.

Values of Test-Statistics, zo, critical statistic are ?? and the decision is to ....

Wages from two small business firms

Observation #	Wages in Firm A ($)	Wages in Firm B ($)	Observation #	Wages in Firm A ($)	Wages in Firm B ($)
1	29363	34035	19	39034	35606
2	39535	31466	20	33363	33632
3	38587	31027	21	29784	37682
4	36103	29679	22	29864	35320
5	34304	38730	23	34093	29587
6	43698	33258	24	39914	30293
7	32119	33979	25	40139	29658
8	37081	32870	26	22099	30544
9	40069	33578	27	37759	36973
10	44344	33946	28	35928	32826
11	36377	28985	29	36832	37557
12	43284	33640	30	30786	25704
13	43229	35110	31	33870	29079
14	29988	34993	32	35884	32816
15	32308	31458	33	40703	30827
16	37747	32321	34	28414	31136
17	32830	30939	35	30870	34792
18	26695	31492	36	34301	34860

		2.578, 1.96, Reject that mu (wage-Firm A) = mu (wage-Firm B).
		2.578, 1.96, Reject that mu (wage-Firm A) > mu (wage-Firm B).
		2.008, 2.58, Fail to Reject that mu (wage-Firm A) = mu (wage-Firm B).
		None of the above

Answer 1

Solution :

The table given shows data of two random samples of employee wages taken from two small business firms providing the same service. The issue to be evaluated is whether the average wage in these two firms is the same. Test this hypothesis at α = 0.05.

The hypotheses of interest here are :

where , , are the means of the wages two Firms A and B respectively.

The appropiate test statistic is given as ,

where , , are the sample sizes for the two samples respectively.

   are the sample means for the two samples respectively.

is the pooled sample standard deviation given as ,

where , are the Sample Standard Deviations respectively.

Rejection Rule : We Reject H₀ at \alpha level of significance, iff,

Calculations : From the data given , we have the following information ,

  

The value of the test statistic is given as ,

The critical value is given as , considering ,

Conclusion : Clearly , we have , thus , we REJECT H₀ at =0.05 level of significance and conclude on the basis of the given data that the two means differ significantly.

Thus , the correct option is OPTION (A) but ideally the Critical Value will be = 1.994437 because , here the Variances are unknown and we are estimating them ........................................ (Ans)

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