Question
In: Statistics and Probability
A simple random sample of 60 items resulted in a sample mean of 80. The population...
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is 15.
At 95% confidence, what is the margin of error (to 4 decimals)?
-
What is the standard error of the mean (to 4 decimals)?
-
Which statement should you use to explain the 95% confidence interval ?
Group of answer choices:
A. We are confident that 95% of population are in the confidence interval
B. We are 95% confident that the confidence interval includes the sample mean.
C. We are 95% confident that the confidence interval includes the population.
D. There is a 95% probability that the population mean lies within the confidence interval.
Solutions
Expert Solution
olution :
Given that,
Point estimate = sample mean = 
= 80
Population standard deviation = 
= 15
Sample size = n = 60
A) At 95% confidence level
= 1 - 95%
= 1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.96
Margin of error = E = Z/2
* ( 
/
E = 1.96 * ( 15 /
E = 3.7955
B) 
=
/ 
n = 15 /
60 = 1.9365
At 95% confidence interval estimate of the population mean is,
±
E
80 ± 3.7955
( 76.2045, 83.7955 )
C. We are 95% confident that the confidence interval includes the population.
orchestra answered 1 year agoRelated Solutions
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