The following random sample from a population whose values were normally distributed was collected.
The 95% confidence interval for $\mu$ is
A)8.52 to 10.98
B)7.75 to 12.25
C)9.75 to 10.75
D)8.00 to 10.00

Question

The following random sample from a population whose values were normally distributed was collected.  
The 95% confidence interval for $\mu$ is
A)8.52 to 10.98 
B)7.75 to 12.25 
C)9.75 to 10.75 
D)8.00 to 10.00

Quizplus · Accepted Answer

Since the sample size is quite large (n=25), we can use the z-distribution and the formula:
CI = sample mean ± (z* standard error)
We calculate the sample mean to be 10, and the standard error to be 0.8916 (using the formula: standard deviation / sqrt(n)). 
The z-value for a 95% confidence level is 1.96. 
Plugging in the values, we get the 95% confidence interval for μ to be:
10 ± (1.96 * 0.8916) which is approximately equal to (7.75, 12.25).
Therefore, the best choice is B.

The Following Random Sample from a Population Whose Values Were μ\muμ

The Following Random Sample from a Population Whose Values Were $\mu$