The quality control department of a paper company measures the brightness (a mea
ID: 3045811 • Letter: T
Question
The quality control department of a paper company measures the brightness (a measure of reflectance) of finished paper on a periodic basis throughout the day. Two instruments are used to measure the paper specimens. Use the following data to test the hypotheses at the a = .05 level that the two instruments
a)have the same variance.
b)have the same mean.
For both tests show what the critical value(s) is.
Instrument 1
Instrument 2
56
59
46
33
52
53
55
38
47
56
55
52
54
47
52
32
48
48
54
51
59
54
55
19
51
51
56
38
48
58
51
42
61
47
66
48
59
54
51
32
59
36
63
44
57
35
53
58
46
45
Instrument 1
Instrument 2
56
59
46
33
52
53
55
38
47
56
55
52
54
47
52
32
48
48
54
51
59
54
55
19
51
51
56
38
48
58
51
42
61
47
66
48
59
54
51
32
59
36
63
44
57
35
53
58
46
45
Explanation / Answer
A ) We want to use F - test for comparison of variance :
Test of Hypothesis :
H0 : The both instrument have the same variance.
against,
H1 : The both instrument have the differant variance.
Test statistic,
Decision Rule : From the above results the p-value (0.000903778 ) is less than level of significance ( alpha = 0.05) . We reject the null hypothesis at 5 % l.o.s.
I.e Variance of both instrument are differant.
B ) For checking mean diffrance we use T-Test here ( t-test for unequal variance)
Test of Hypothesis :
H0 : The both instrument have the same Mean.
against,
H1 : The both instrument have the differant Mean.
Test statistic,
Decision Rule : From the above results the p-value (0.000187738 ) is less than level of significance ( alpha = 0.05) . We reject the null hypothesis at 5 % l.o.s.
I.e Mean of both instrument are differant.
>>>>>>>>>>>>>> Best Luck >>>>>>>>>>>>>
F-Test Two-Sample for Variances Variable 1 Variable 2 Mean 54.16 45.2 Variance 27.22333333 103.0833333 Observations 25 25 df 24 24 F 0.264090542 P(F<=f) one-tail 0.000903778 F Critical one-tail 0.504093347Related Questions
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