Question

Construct a 95​% confidence interval to estimate the population mean with x=101 and σ=27 for the following sample sizes.

​a)	n	equals=	3030
​b)	n	equals=	4343
​c)	n	equals=	6464

​a) With 95​% ​confidence, when n=30​, the population mean is between the lower limit of

and the upper limit of.

​(Round to two decimal places as​ needed.)

​b) With95​% ​confidence, when n=43​, the population mean is between the lower limit of

and the upper limit of.

​(Round to two decimal places as​ needed.)

​c) With 95​% ​confidence, when n=64​, the population mean is between the lower limit of

and the upper limit of.

Answer 1

Given that, sample mean $(\bar x)$ = 101

population standard deviation $(\sigma)$ = 27

We want to find, the 95% confidence interval for the population mean for different sample sizes.

Using TI-84 calculator we find these confidence intervals.

​a) With 95​% ​confidence, when n=30​, the population mean is between the lower limit of 91.34 and the upper limit of 110.66

​b) With95​% ​confidence, when n=43​, the population mean is between the lower limit of 92.93 and the upper limit of 109.07

​c) With 95​% ​confidence, when n=64​, the population mean is between the lower limit of 94.39 and the upper limit of 107.61