Estimation and Confidence intervals

Question

A sample of 85 observations is taken from a normal population with a standard deviation of 52. The sample mean is 57. Determine the 98% confidence interval for the population mean. (Round the final answers to 3 decimal places.)

Answer 1

The confidence interval is defined as:

 

Mean Value +/- (z-value corresponding to 98%)* Standard Error of Estimation

 

Sample Mean Value = 57

 

Z value corresponding to 98% = 2.326348

 

Standard Error of Estimation = Standard Deviation/(sample size)^1/2

 

Plugging in all values:

 

57 +/- (2.326348)*(52/(85)^1/2) = 57 +/- 13.12104915 or 

 

98% Confidence Interval is [43.87895085, 70.12104915]