Construct the confidence interval for the population mean u. C equals 0.95, X equals 16.2, o= 8.0, and N equals 85. a 95% confidence interval for u is [ ], [ ]. Round to one decimal place as needed.

Question

Construct the confidence interval for the population mean u. C equals 0.95, X equals 16.2, o= 8.0, and N equals 85. a 95% confidence interval for u is [   ], [   ]. Round to one decimal place as needed.

3mar · Answer

@IrishBoy123 
If you could help here, I would be grateful!
Thanks in advance.

irishboy123 · Answer

For a big enough normal distribution, ie $\bar x  = \mu = 16.2$.  The sample and population means are the same.

And common sense suggests there is no point other than starting there.

From z-scores, about $ 95 \%$ of the data points will lie within $\pm 2 \sigma$'s of the mean, ie confidence interval, ie $x \in [ \mu - 2 \sigma , \mu + 2 \sigma]$

We adjust the variance as : $\sigma^2 =  \sigma_{normalised }^2  =  \dfrac{\sigma_{sample}^2}{N} $ where $N = 85$

so that $\sigma \approx 0.87$

meaning that:
$x \in [ 14.46 , 17.94]$

or so  I **reckon**

:)

3mar · Answer

Thank you for good explanation 

+ Thank you for your quick response!