A new device is being developed for measurement of plasma glucose concentration intended

to cover the range $63197$ mg$/$dL$.$ A prototype for the device has been completed, with an

output display indicating the estimated concentration level, denoted $.$ To calibrate the

device, the true concentration, denoted $,$ is manipulated experimentally and the indicated

values are recorded.

A$.$ In a first experiment, the true concentration is set to a fixed value of $130$ mg$/$dL and $10$

repeated measurements of the indicated concentration are recorded:

$=[130\mathrm{.}79,128\mathrm{.}64,122\mathrm{.}73,132\mathrm{.}52,130\mathrm{.}5,...$

$138\mathrm{.}14,124\mathrm{.}36,129\mathrm{.}15,126\mathrm{.}08,131\mathrm{.}69]$ mg$/$dL

i$.$ Compute the device$$s bias error and precision error.

ii$.$ If it is determined that the bias and precision error computed above are of a fixed

magnitude across the device$$s operating range, then given an indicated value of $152$

mg$/$dL$,$ what would be its $95\%$ confidence interval?

B$.$ In another similar device, it is found that there is a bias error that varies over the input

range and that differs depending on whether the input is ascending versus descending.

It is determined that the best fitting polynomial of the input$-$output curve $($i$.$e$.,$ vs$.)$ is

given by

$=0\mathrm{.}0221\mathrm{.}2+300/$

when the true concentration is ascending, and

$=0\mathrm{.}022+9\mathrm{.}2196\mathrm{.}44/$

when the true concentration is descending. Compute the $\%$ hysteresis of the device.