Question

Based on the "Times" data, is the proposed method of production lower variance than the current?

Select one: a. Yes, the F statistic is greater than the F critical for a one tail test at the 95% confidence level. b. Yes, because the current variance is 2.5 times the variance of the proposed method. c. No, because the p value is very small. d. No, because the f critical is below 2.

Additional Info:

Current	Proposed
76	74
76	75
77	77
74	78
76	74
74	80
74	73
77	73
72	78
78	76
73	76
78	74
75	77
80	69
79	76
72	75
69	72
79	75
72	72
70	76
70	72
81	77
76	73
78	77
72	69
82	77
72	75
73	76
71	74
70	77
77	75
78	78
73	72
79	77
82	78
65	78
77	76
79	75
73	76
76	76
81	75
69	76
75	80
75	77
77	76
79	75
76	73
78	77
76	77
76	77
73	79
77	75
84	75
74	72
74	82
69	76
79	76
66	74
70	72
74	78
72	71

Answer 1

Data:       

n1 = 61      

n2 = 61      

s1^2 = 6.281967      

s2^2 = 15.5623      

Hypotheses:      

Ho: σ1^2 = σ2^2      

Ha: σ1^2 < σ2^2      

Decision Rule:      

α = 0.05      

Numerator DOF = 61 - 1 = 60    

Denominator DOF = 61 - 1 = 60    

Critical F- score = 0.651757     

Reject Ho if F < 0.651757     

Test Statistic:      

F = s1^2 / s2^2 =   6.281967/15.5623 =    0.4037

p- value = 0.0003

Decision (in terms of the hypotheses):    

Since 0.403666 < 0.6518 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence that the proposed method of production has significantly lower variance than the current.

You can mark option (a) as the answer.