Question

Find a 95% confidence interval for predicting the mean length of fish in a particular pond if the sample data contained the following length in centimeters

23 45 43 34 26 36 67 45 43 55 53 42 87 65 45 51 53 54 54 48 49 54 53 52 54

Answer 1

We can find the sample mean and standard deviation of the given data set using excel function =AVERAGE( ) and =STDEV.S() respectively.

So sample mean   = 49.24 and sample standard deviation (s) = 12.8915

Confidence interval is given by,

Lower bound =    - E

Upper bound =    + E  

E =     ; t is critical value follows t distribution with degrees of freedom (df) = n-1

We are given confidence level = 0.95  

We can find critical value using excel function =TINV( α , d.f )

α = 1 - confidence level = 1 - 0.95 = 0.05

degrees of freedom (d.f) = n - 1 = 25-1 = 24

t =TINV(0.05,24)

t = 2.064

Therefore,

E =  

E = 5.3216

Lower bound =    - E = 49.24 - 5.3216 = 43.9184

Upper bound =    + E = 49.24 + 5.3216 = 54.5616

Therefore 95% confidence interval for predicting the mean length of fish in a particular pond is ( 43.9184 , 54.5616 )