You measure 28 turtles' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 11.9 ounces. Based on this, construct a 90% confidence interval for the true population mean turtle weight. Give your answers as decimals, to two places.
Solution :
Given that,
Point estimate = sample mean =
= 64
Population standard deviation =
= 11.9
Sample size = n =28
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.1
/ 2 = 0.1 / 2 = 0.05
Z/2 = Z0.05 = 1.645 ( Using z table )
Margin of error = E = Z/2
* (
/n)
= 1.645* ( 11.9/
28)
= 3.70
At 90% confidence interval estimate of the population mean
is,
- E <
<
+ E
64- 3.70 <
< 64+ 3.70
60.30 <
< 67.70
(60.30 , 67.70)
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