Question

Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.

Test scores: n = 81,  = 69.0, σ = 4.6; 98% confidence

Answer 1

Solution :

Given that,

Point estimate = sample mean =    =69

Population standard deviation =    = 4.6

Sample size = n =81

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * ( 4.6 /  81 )

= 1.19
At 98% confidence interval estimate of the population mean
is,

- E < < + E

69- 1.19 <   < 69 + 1.19

67.81 <   < 70.19