Question

Median = 1.540

mean=1.510

Sample size = 100

a) Find a 95% confidence interval for the mean of the transformed data.

b) Back-transform your answer in c) to give an approximate 95% confidence interval for the median age of North American Black Bears in British Colombia.  Interpret this in context.          

Answer 1

a)

we know that the confidence interval is given as

mean +- z*sd/sqrt(n)

where n is the sample size , 100
mean = 1.540

and median = 1.510

here you shpuld calculated the sd of the data

and also from the z tables we know that the z value for 95% CI is 1.96

put the values in the above equation and solve for

Upper limit = mean + z*sd/sqrt(n)
lower limit = mean - z*sd/sqrt(n)

CI tells us that we are 95% confiedent that the true value of the mean would lie in the interval given by

lower limit , upper limit

b)

It is not given what transformation was used in the data . However in order to back transform , you simply need to reverse the mathematical calculations
for example
if log transformation was done , then you need to take "exp" of the log data to get the original data

if square root was done , then take square of the transformed data