Question # During the production of boiler plate, test pieces are subjected to a load, and their elongations are measured. In one particular experiment, five tes

Confidence intervals
ANSWERED During the production of boiler plate, test pieces are subjected to a load, and their elongations are measured. In one particular experiment, five tests will be made, at loads (in MPa) of 11, 37, 54, 70, and 93. The least-squares line will be computed to predict elongation from load. Confidence intervals for the mean elongation will be computed for several different loads. Which of the following intervals will be the widest? Which will be the narrowest? i. The 95% confidence interval for the mean elongation under a load of 53 MPa. ii. The 95% confidence interval for the mean elongation under a load of 72 MPa. iii. The 95% confidence interval for the mean elongation under a load of 35 MPa. 2021-06-01
Given data values: 11,37,54,70,93
The mean is the sum of all values divided by the number of values:
$$\displaystyle\overline{{x}}={\frac{{{11}+{37}+{54}+{70}+{93}}}{{{5}}}}={\frac{{{265}}}{{{5}}}}={53}$$
Predictions for z-values closest to the sample mean & are the most reliable. The more reliable the prediction, the narrower the confidence interval will be.
The widest confidence interval is then for the c-value that is furthest from the sample mean © = 53, which is the value 72 MPa.
The narrowest confidence interval is then for the x-value that is closest to the sample mean $$\displaystyle\overline{{x}}={53}$$, which is the sample mean of 53 MPa itself