Question

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An experiment with artillery shells yields the following data on the characteristics of lateral deflections and ranges. Would you conclude that deflection and range are independent? Use a = 0.430. What is the P-value for this test? Round your answer to three decimal places (e.g. 98.765). Lateral Deflection Range (yards) Left Normal Right 0-1,999 6 14 8 2,000-5,999 9 11 4 6,000-11,999 8 17 6 The evidence sufficient to claim that the data are dependent. P-value =

Answer 1

H0: Deflection and range are independent
H1: Deflection and range are not independent

Let the los be alpha = 0.430

The observed frequencies are

	Lateral deflection
Range	Left	Normal	Right	Total
0 - 1999	6	14	8	28
2000 - 5999	9	11	4	24
6000 -11999	8	17	6	31
Total	23	42	18	83

The expected frequencies are

Range	Left	Normal	Right	Total
0 - 1999	7.759	14.169	6.072	28
2000 - 5999	6.651	12.145	5.205	24
6000 -11999	8.59	15.687	6.723	31
Total	23	42.001	18	83

The chi-square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
6	7.759	0.3988
14	14.169	0.002
8	6.072	0.6122
9	6.651	0.8296
11	12.145	0.1079
4	5.205	0.279
8	8.59	0.0405
17	15.687	0.1099
6	6.723	0.0778
	Total:	2.4577

Degrees of freedom: 4

Test Statistic, X^2: 2.458

The evidence to not sufficient to claim that the data are dependent

P-Value: 0.652

since P-value > alpha 0.430 so we accept H0 i.e. Deflection and range are independent