In: Statistics and Probability
You measure 29 turtles' weights, and find they have a mean weight of 38 ounces. Assume the population standard deviation is 3.2 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight. Give your answers as decimals, to two places
Solution :
Given that,
sample mean =
= 38
Population standard deviation =
= 3.2
Sample size = n =29
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576 ( Using z table )
Margin of error = E = Z/2* ( /n)
= 2.576 * (3.2 / 29)
= 1.53
At 99% confidence interval estimate of the population mean is,
- E < < + E
38-1.53 < < 38+1.53
36.47< < 39.53
(36.47 , 39.53)