Question

The driving distances (in miles) to work of 30 people are shown below. Assume the population standard deviation is 8 miles.
Construct a 95% confidence interval

12 9 7 2 8 7 3 27 21 10 13 7 2 307 6 13 6 4 1 10 3 13 6 2 9 2 12 16 18 Contuoto00onfidence interval c

Answer 1

We have given a population standard deviation for driving distance is =   miles

0 = 8

Driving distance of 30 peoples are given in example

X ΣΧ, n
  $= \frac{1}{30} * \sum{(12+9+ ... + 18)}$

$\bar{X} =\frac{282}{30} = 9.4$

Here population standard deviation is known so we use Z-distribution while calculating confidence interval.

95% confidence , $\alpha = 0.05 , Z_{\alpha} = 1.96$    ... { Two sided}

Confidence interval for population mean is given by

$\bar {X} \pm E$ , Where E= margin of error

$E = Z_{\alpha}*\sigma/\sqrt{n}= 1.96*8/\sqrt{30} = 2.8628$

Lower Limit =   $\bar {X} - E = 9.4 -2.8628 =6.5372$

Upper Limit = $\bar {X} + E = 9.4 + 2.8628 =12.2628$

95% confidence interval for population mean is (6.5372,12.2628)