An article in Technometrics (1999, Vol. 41, pp. 202-211) studied the capability

Question

An article in Technometrics (1999, Vol. 41, pp. 202-211) studied the capability of a gauge by measuring the weights of two sheets of paper. The data are shown below. Check the assumption that the data from each sheet are from normal distributions. Test the hypothesis that the mean weight of the two sheets are equal against the alternative that they are not (and assume equal variances). Use alpha = 0.05 and assume equal variances. Find the P-value. Repeat the previous test with alpha = 0.10. Compare your answers for parts (b) and (c) and explain why they are the same or different. Explain how the questions in parts (b) and (c) could be answered with confidence intervals.

Explanation / Answer

Group Paper 1 Paper 2
Mean 3.47200 3.24940
SD 0.00831 0.00714
SEM 0.00214 0.00184
N 15 15

The test hypothesis is
Ho:1=2
Ha:1 not equal to 2

The test statistic is

t=(xbar1 - xbar2)/[s1^2/n1 + s2^2/n2]

=(3.472-3.2494)/sqrt(0.00831^2/15 + 0.00714^2/15)

= 78.69

P-value is less than 0.0001

Since p-value is smaller than a=0.025, we reject Ho.

So we can conclude that the mean weight of the two sheets are not equal.

The 95% confidence interval is

From 0.21681 to 0.22839

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