Question

For each exercise, answer the following along with any additional questions.  Select and justify the best test(s). The chi-square, Phi, Yates, or Lambda (or even a combination) might be best for a problem given the data and research question. Do not assume the independent is always on the row.  Provide the null and alternative hypotheses in formal and plain language for the appropriate test at the 0.05 significance level.  Do the math and reject/retain null at a=.05. State your critical value.  Explain the results in plain language.

The State of Arkansas information technology director is considering a new sole source contract for the state’s microcomputer purchases. One factor is reliability. As a test, the director samples 62 state government computers across the three bidding companies and notes whether the computer broke before the warranty expired. (C15PROB4.SAV)

Required Repair Before Warranty Expired?

Microcomputer Yes No

SunPro 8 10

ICM 7 21

Dellix 8 8

  

Answer 1

The hypothesis being tested is:

H₀: The computer did not broke before the warranty expired

H_a: The computer broke before the warranty expired

		Yes	No	Total
SunPro	Observed	8	10	18
	Expected	6.68	11.32	18.00
	O - E	1.32	-1.32	0.00
	(O - E)² / E	0.26	0.15	0.42
ICM	Observed	7	21	28
	Expected	10.39	17.61	28.00
	O - E	-3.39	3.39	0.00
	(O - E)² / E	1.10	0.65	1.76
Dellix	Observed	8	8	16
	Expected	5.94	10.06	16.00
	O - E	2.06	-2.06	0.00
	(O - E)² / E	0.72	0.42	1.14
Total	Observed	23	39	62
	Expected	23.00	39.00	62.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	2.08	1.23	3.31
		5.991	critical value
		3.31	chi-square
		2	df

The test statistic is 3.31.

The critical value is 5.991.

Since 3.31 < 5.991, we fail to reject the null hypothesis.

Therefore, we cannot conclude that the computer broke before the warranty expired.