Question

A study of 40 white mice

showed that their average
weight was 3.20 ounces. The
standard deviation of the
population is 0.8 ounces. Which
of the following is the 80%
confidence interval for the mean
weight per white mouse?

Answer 1

`3.20-1.304(0.8)/(√(40))=3.035`

`3.20+1.304(0.8)/(√(40))=3.365`

And the confidence interval would be between (3.035;3.365)

Explanation:

Information given

`\bar X=3.20` represent the sample mean

`\mu` population mean (variable of interest)

s=0.8 represent the sample standard deviation

n=40 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

`\bar X \pm t_(\alpha/2)(s)/(√(n))` (1)

The degrees of freedom are given by:

`df=n-1=40-1=39`

The Confidence level is 0.80 or 80%, the significance would be
`\alpha=0.2` and
`\alpha/2 =0.1`, and the critical value would be
`t_(\alpha/2)=1.304`

Now we have everything in order to replace into formula (1):

`3.20-1.304(0.8)/(√(40))=3.035`

`3.20+1.304(0.8)/(√(40))=3.365`

And the confidence interval would be between (3.035;3.365)