In: Statistics and Probability
A sample of 7 adult elephants had an average weight of 11900 pounds. The standard deviation for the sample was 24 pounds. What is the 99% confidence interval of the population mean for the weights of adult elephants? Assume that the variable is normally distributed.
n = sample size = 7
s = sample standard deviation = 24
The formula for a confidence interval
E = margin of error
df = degrees of freedom = n-1 = 7 - 1 = 6
c = level of confidence = 0.990 ( We converted 99% in to decimal )
We use t table to find t critical value
We look for row headed df = 6 and column headed c = 0.990
So we get t critical value
E =33.62674323
Final answer:-
The confidence interval of the population mean for the weights of adult elephants is ( 11866.37326, 11933.62674 )
Or
Note: If they mention any rounding then round according to instruction.