Question

show data visualizations and comment .

create data visualizations before and after the results that you would present for the following:

1)Analyze the correlation for the following data:

Orifice Diameter	Radon Released (%)
0.37	80	83	83	85
0.51	75	75	79	79
0.71	74	73	76	77
1.02	67	72	74	74
1.40	62	62	67	69
1.99	60	61	64	66

2)A company operates four machines three shifts each day. From production records, the following data on the number of breakdowns are collected:

Shift	Machines
	A	B	C	D
1	41	20	12	16
2	31	11	9	14
3	15	17	16	10

Test the hypothesis (using ? = 0.05) using the Chi-Square Test that breakdowns are independent of the shift. Find the p-value for this test.

Answer 1

Ans:

2)

H_o:Breakdowns are independent of the shift.

Ha:Breakdowns are not independent of the shift.

Expected count=row sum*column sum/overall toal

	Observed count(fo)
Shift/Machines	A	B	C	D	Total
1	41	20	12	16	89
2	31	11	9	14	65
3	15	17	16	10	58
Total	87	48	37	40	212
	Expected count(fe)
Shift/Machines	A	B	C	D	Total
1	36.52	20.15	15.53	16.79	89
2	26.67	14.72	11.34	12.26	65
3	23.80	13.13	10.12	10.94	58
Total	87	48	37	40	212
	Chi square=(fo-fe)^2/fe
Shift/Machines	A	B	C	D	Total
1	0.55	0.00	0.80	0.04	1.39
2	0.70	0.94	0.48	0.25	2.37
3	3.25	1.14	3.41	0.08	7.89
Total	4.50	2.08	4.70	0.36	11.65

Test statistic:

Chi square score=11.65

df=(3-1)*(4-1)=6

p-value=CHIDIST(11.65,6)=0.0703

As,p-value>0.05,we fail to reject the null hypothesis and we can conclude that breakdowns are independent of the shift.