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 ChiSquare Test that breakdowns are independent of the shift. Find the pvalue for this test.
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=(fofe)^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=(31)*(41)=6
pvalue=CHIDIST(11.65,6)=0.0703
As,pvalue>0.05,we fail to reject the null hypothesis and we can conclude that breakdowns are independent of the shift.
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