Question

b) Cvil engineers have developed 3Dmodel to predict the response of jointed concrete pavements to teaperature variations. To check this model, they measured the change in trave table below was ob erent occasions and compared this to the modelled values. The ange in Strain Modelled Measurement Fie asurement 58 69 35 -32 -40 52 59 32 Jul 25 Aug 4 Aug 16 Sep 3 Oct 26 Nov 3 39 71

Answer 1

i) Since measurements are taken on the same unit, the observations are correlated and hence the data is paired.

ii) Null hypothesis: Population means of the measurements are the same

Alternative hypothesis:  Population means of the measurements differ

Paired t statistic is T=$\sqrt{n}(\bar{d}-0)/s_d$, where

$\bar{d}$ is the sample mean of differences, s_d is the SD of the differences, n=sample size=6

Then two sided p value is obtained as .508, which is more than 5%.

Thus the evidence is not strong against the null and we fail to reject the null. Thus population means of the measurements do not differ significantly.

iii) The probability plot shows almost all points lying on the straight line and hence evidence of normality seems to be strong enough. Further, we perform a test of normality.

Null hypothesis: Distribution of the differences is normal

Alternative hypothesis:  Distribution of the differences is not normal

We performed Anderson Darling test for normality.

We obtain from the output, value of the test statistic, .170 and p value .879.

Thus evidence against the normality is very weak and hence we fail to reject the null hypothesis. Thus the distribution of the differences is not significantly different from normal.