floymdiT

2021-03-11

The local energy company claims the average annual electricity bill for its subscribers is just $600. A consumer watchdog group wants to dispute this claim. All agree that the standard deviation sigma of annual electricity bills is$150.
Some time later, a wealthy activist provides funding for a simple random sample of 250 households. The average annual electricity bill for this sample is \$622. Find a $95\mathrm{%}$ confidence interval for the true mean annual electric bill, based on this sample.

Demi-Leigh Barrera

Step 1
It is assumed that the sample mean is 622 and the population standard deviation is 150.
Step 2
From the given information, the confidence level is 0.95 and the level of of significance
The $95\mathrm{%}$ confidence interval for the true mean is obtained as follows:
$95\mathrm{%}CI=\stackrel{―}{x}±{z}_{\frac{\alpha }{2}}\left(\frac{\sigma }{\sqrt{n}}\right)$
$=622±{z}_{\frac{0.05}{2}}\left(\frac{150}{\sqrt{250}}\right)$
$=622±1.96\left(\frac{150}{\sqrt{250}}\right)$

$=\left(603.4058,640.5942\right)$

Do you have a similar question?