Question

A person gets on and off a bathroom scale four times. The four readings (in pounds) are 148, 151, 150, and 152. Each time after the person gets off the scale, the reading is 2 lb. Is it possible to estimate the uncertainty in these measurements? If so, estimate it. If not, explain why not. Is it possible to estimate the bias in these measurements? If so, estimate it. If not, explain why not.

Answer 1

Answer:

See explanation below

Step-by-step explanation:

Since each time after the person gets off the scale, the reading is 2 lb the person's weight must be near the mean of

148-2, 151-2, 150-2, 152-2; that is to say, near the mean of 146, 149, 148, 150 = (146+149+148+150)/4 = 148.25

We could estimate the uncertainty as the standard error SE

$\bf SE=\frac{s}{\sqrt{n}}$  

where  

s = standard deviation of the sample

n = 4 sample size.

Computing s:

$\bf s=\sqrt{\frac{(146-148.25)^2+(149-148.25)^2+(148-148.25)^2+(150-148.25)^2}{4}}=1.479$

So, the uncertainty is 1.479/2 = 0.736

It is not possible to estimate the bias, since it is the difference between the true weight and the mean, but we do not know the true weight.