The following data concern the thickness of nonmagnetic coatings of zinc. Two me
ID: 3363954 • Letter: T
Question
The following data concern the thickness of nonmagnetic coatings of zinc. Two measurements are made on the same specimen, the first using a nondestructive method, the second a destructive method.
Specimen
1
2
3
4
5
6
7
8
9
10
11
Nondestructive method
105
120
85
181
115
127
630
155
250
310
443
Destructive method
116
132
104
139
114
129
720
174
312
338
465
a) At the 0.05 level of significance, test to see if there is a significant difference in the two methods. (to be done by hand)
b) What assumption is necessary to perform the test in part a)?
c) Verify your work in part (a) by conducting the appropriate confidence interval. (to be done by hand)
Specimen
1
2
3
4
5
6
7
8
9
10
11
Nondestructive method
105
120
85
181
115
127
630
155
250
310
443
Destructive method
116
132
104
139
114
129
720
174
312
338
465
Explanation / Answer
The means of Group 1 and Group 2 are not significantly different at p < 0.05.
b). Assumption :-
c). Confidence interval -
Group 1 - For undestructive method
M = 229.1818
t = 1.96
sM = (171.10572/11) = 51.59
= M ± Z(sM)
= 229.1818 ± 1.96*51.59
= 229.1818 ± 101.115149
Result
M = 229.1818, 95% CI [128.066651, 330.296949].
You can be 95% confident that the population mean () falls between 128.066651 and 330.296949.
Group 2 - Destructive method
Calculation
M = 249.3636
t = 1.96
sM = (195.73932/11) = 59.02
= M ± Z(sM)
= 249.3636 ± 1.96*59.02
= 249.3636 ± 115.672409
Result
M = 249.3636, 95% CI [133.691191, 365.036009].
You can be 95% confident that the population mean () falls between 133.691191 and 365.036009.
Group 1 Group 2 Mean 229.1818 249.3636 Variance 29277.1636 38313.8546 Stand. Dev. 171.1057 195.7393 n 11 11 t -0.2575 degrees of freedom 20 critical value 2.086Related Questions
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