Question

If you measure a quantity four times and the standard deviation is 1.0% of the average, can you be 90% confident that the true value is within 1.2% of the measured average?

Short answer

Yes, there is a 90% confidence level that the true value is within 1.2% of the measured average.

Step-by-step solution

Objective

The goal of this problem is to check whether the confidence interval for the true value is within 1.2% of the measured average at 90% confidence level.This means, $\frac{ts}{\sqrt{n}}\approx 1.2\%\overline{x}$or $0.012\overline{x}$

Determine the confidence Interval

Now, to solve, we will use the formula of the confidence interval (CI) :

$\mathrm{CI}\mathrm{for}\mathrm{\mu }=\overline{\mathrm{x}}\pm \frac{\left(2.353\right)\left(0.01\overline{\mathrm{x}}\right)}{\sqrt{4}}=\overline{\mathrm{x}}\pm 0.0118\overline{\mathrm{x}}\approx 0.012\overline{\mathrm{x}}$is obtained from

Table 4 - 4 ; the degrees of freedom = 3 at 90 % confidence level.