SELECT ALL THAT APPLY.
-If the sample standard deviation of a sample N = 1001 is 2.60 and sample mean is 2.94,then
A)estimate standard error is .8.
B)the upper bound with 95% confidence level is 3.10.
C)the lower bound with 95% confidence level is 2.78.
D)the Z value corresponding to a 95% confidence level is 2.58.

Question

Quizplus · Accepted Answer

Using the formula for the confidence interval: 
Confidence interval = sample mean ± (Z value x standard error)
We can calculate the standard error as follows:
Standard error = sample standard deviation / square root of sample size
Standard error = 2.60 / sqrt(1001) = 0.0823

The Z value corresponding to a 95% confidence level is 1.96 (not 2.58 as stated in choice D).

Thus, the confidence interval is: 
2.94 ± (1.96 x 0.0823)

The upper bound is 3.10 (2.94 + 0.16) 
The lower bound is 2.78 (2.94 - 0.16)

Therefore, choices B and C are correct. Choice A is incorrect as it gives an incorrect estimate of the standard error. Choice D is incorrect as it provides an incorrect value for the Z value.