Answer:
We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2 is between (2.793; 3.951)
Step-by-step explanation:
Data provided
2.69, 5.76, 2.67, 1.62, and 4.12
We can calculate the sample mean with this formula:
![\bar X =\frac{\sum_{i=1}^n X_i}{n}](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D)
And replacing we got:
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n=5 represent the sample size
Confidence interval
:
The two sided confidence interval for the true mean is given by:
(1)
We have the confidence level given of 0.95 or 95%, the value of
and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
Replacing into the formula for the interval we have this:
We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2 is between (2.793; 3.951)