Question
In: Statistics and Probability
Forty items are randomly selected from a population of 450 items. The sample mean is 29,...
Forty items are randomly selected from a population of 450 items. The sample mean is 29, and the sample standard deviation 2. Develop a 95% confidence interval for the population mean. (Round the final answers to 2 decimal places.)
The confidence interval is between and .
Solutions
Expert Solution
Solution :
Given that,
= 29
s =2
n = 450
Degrees of freedom = df = n - 1 =450 - 1 = 449
a ) At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/
2= 0.05 / 2 = 0.025
t
/2,df = t0.025,449 = 1.965 ( using student t
table)
Margin of error = E = t/2,df
* (s /
=1.965 * ( 2/
= 0.19
The 95% confidence interval estimate of the population mean is,
- E < 
<
+ E
29 -0.19 <
<29 + 0.19
28.81 <
< 29.19
(28.81 ,29.19 )
orchestra answered 2 years agoRelated Solutions
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