- The waiting times, in minutes, of patients at a doctor's surgery follows a normal distribution with unknown mean \(\mu\) and known standard deviation \(\sigma\)
A random sample of 120 patients was taken.
- Find, in the form \(k \sigma\), the width of a \(99 \%\) confidence interval for \(\mu\) based on this sample. Give the value of \(k\) to 2 decimal places.
A further random sample of 100 patients from the surgery gave a \(90 \%\) confidence interval for \(\mu\) of \(( 5.14,6.25 )\)
- Use this confidence interval to determine whether or not it provides evidence that \(\mu = 6\)
State the hypotheses being tested here and write down the significance level being used. You do not need to carry out any further calculations.
- Find the value of \(\sigma\)