Question

In: Statistics and Probability

The modulus of elasticity of structural components was measured one minute after loading. The same samples...

The modulus of elasticity of structural components was measured one minute after loading. The same samples were tested again after 4 weeks. The following table shows the values of modulus of elasticity in both cases.Conduct an appropriate hypothesis test for the true average difference between the modulus in the two cases. Clearly state your conclusions.. Data is also available

Sample Number After 1 minute After 4 weeks
1 10490 9110
2 16620 13250
3 17300 14720
4 15480 12740
5 12970 10120
6 17260 14570
7 13400 11220
8 13900 11100
9 13630 11420
10 13260 10910
11 14370 12110
12 11700 8620
13 15470 12590
14 17840 15090
15 14070 10550
16 14760 12230

Solutions

Expert Solution

In this case we cannot make use of independent samples t-test, rather we will make use of a paired t-test.

Let the subscript 1 denote the reading after 1 minute, and 2 denote the readings after 4 weeks.

The hypotheses are:

H0: 1 = 2

Ha: 1 > 2

The results as obtained from excel are shown below:

As seen in the result above, the p-value (shown in green) for this one tailed hypothesis test is much less than the significance level of 0.05

Thus the result is significant, and we have to reject the null hypothesis.

Thus there is significant evidence that modulus of elasticity has decreased for the group in which reading is taken after 4 weeks.

orchestra answered 2 years ago
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