Use the mean and the standard deviation obtained from the last module and test the claim that the mean age of all books in the library is greater than 2005. Share your results with the class.
We have 100 data points.
We build a confidence interval for the Mean age of all books.
100 data point being x1,x2,−−−x100
By use of given values, obtain the mean sample and standard deviation Sample
The exact formula is —
Mean Sample =Xˉ=n∑x
Standard deviation Sample =s=n−1∑x2−n(∑x)2
We conclude that the sample size is large; thus, we can assume Sample mean to follow a normal distribution way—
The confidence interval is given as following —
(Xˉ−E, Xˉ+E )
Upper limit =Xˉ+E
Lower limit =Xˉ−E
In a case where E is the margin of error,
the formula of the margin of error is as follows:
Letter n = 100 , degree of freedom = n-1 = 99
Letter α = level of significance,
95% confidence interval, α = 0.05
99% confidence interval, α = 0.01
68% confidence interval, α = 0.32
(To obtain the critical value of t, i.e., tα/2,n−1 using t distribution table and excel software)
The above is the primary method used to obtain a confidence interval for all books’ mean age books.