Suppose seven measurements of the temperature in a controlled environment yield the following data (in degrees celsius).
\begin{array}{} 1 & -0.9 & -0.8 & 0.6 & 0.2 & 1.2 & 0.6 \end{array}
assume that the different measurements are due only to measurement error, and that measurement error is normally distributed. the goal is to set up an approximate 90% confidence interval for the correct measurement. in each part, answer correct to three decimal places. calculator recommended.
estimate the correct measurement. degrees celsius
attach a give-or-take value to the estimate (that is, estimate the standard error). degrees celsius
there are 7 measurements. if measurements follow a normal distribution (e. g., if they vary only due to chance measurement error), then the standardized average of 7 measurements follows a student t -distribution with degrees of freedom. so, for 90% confidence, we include standard error(s) on each side of our estimate.
an approximate 90% confidence interval for the correct measurement is
[ , ]