In: Statistics and Probability
In a random sample of 5 residents of the state of Texas, the mean waste recycled per person per day was 1.9 pounds with a standard deviation of 0.89 pounds. Determine the 99%
confidence interval for the mean waste recycled per person per day for the population of Texas. Assume the population is approximately normal.
Step 1 of 2 :
Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
solution
Given that,
= 1.9
s =0.89
n = 5
Degrees of freedom = df = n - 1 = 5- 1 = 4
At 99% confidence level the t is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
t /2 df = t0.005, 4= 4.602 ( using student t table)
Margin of error = E = t/2,df * (s /n)
= 4.602 * (0.89 / 5) = 1.832
The 99% confidence interval estimate of the population mean is,
- E < < + E
1.9 - 1.832< < 1.9 + 1.832
0.068 < < 3.732
(0.068 , 3.732)