Question
In: Statistics and Probability
A survey of 269 students obtaining their study times found a mean of 137 min. with...
A survey of 269 students obtaining their study times found a mean of 137 min. with an assumed standard deviation of 45 min. What is a 99% confidence interval for the population mean?
Question 7 options:
|
(131.6, 142.4) |
|
|
(126.8, 147.2) |
|
|
No answer is correct. |
|
|
(132.5, 141.5) |
|
|
(129.9, 144.1) |
Solutions
Expert Solution
Solution :
Given that,
Point estimate = sample mean = 
= 137
Population standard deviation = 
= 45
Sample size = n = 269
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
Margin of error = E = Z/2*
(
/
= 2.576 * (45 /
= 7.1
At 99% confidence interval estimate of the population mean is,
- E < 
<
+ E
137 - 7.1 <
< 137 + 7.1
129.9 <
< 144.1
(129.1 , 144.1)
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