Two different analytical tests can be used to determine the impurity level in steel alloys. Nine specimens are tested using both procedures, and the results are shown in the tabulation.Find the 95\% confidence interval for the mean difference of the tests, and explain it.

UkusakazaL

UkusakazaL

Answered question

2021-07-31

Two different analytical tests can be used to determine the impurity level in steel alloys. Nine specimens are tested using both procedures, and the results are shown in the following tabulation.
SpecimenTest1Test211.21.421.61.731.51.541.41.351.82.061.82.171.41.781.51.691.41.5
Find the 95% confidence interval for the mean difference of the tests, and explain it.

Answer & Explanation

Cheyanne Leigh

Cheyanne Leigh

Beginner2021-08-03Added 1 answers

Test1(X)Test2(Y)(xx¯)(xx¯)2(yy¯)(ybary)21.21.40.311110.096790.244440.059751.61.70.088890.007900.055560.003091.51.50.011110.000120.144440.020861.41.30.111110.012350.344440.118641.82.00.288890.083460.355560.126421.82.10.288890.083460.455560.207531.41.70.111110.012350.055560.003091.51.60.011110.000120.044440.001981.41.50.111110.012350.144440.02086
The mean x=1nx
Test 1 NKS x=13.69=1.511
Test 2 y=14.89=1.644
σ=1n1(xx)2
Test 1 σ=0.308898=0.1965
Test 2 s2=0.56228=0.2651
The 95% CI
C.I.=(xy)±t0.05, 8s12n1+s22n2
C.I.=(1.5111.644)±2.306(0.1965)29+(0.2651)29
C.I.=[0.387, 0.120]
The true difference between the mean of test 1 and test 2 will lie within -0.387 and 0.120.

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