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 = 104,  = 95.3, σ = 6.5; 99% confidence

Group of answer choices

a. 94.2 < μ < 96.4

b. 93.7 < μ < 96.9

c. 93.8 < μ < 96.8

d. 94.1 < μ < 96.5

Answer 1

Solution

Given that,

= 95.3

= 6.5

n = 104

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* (/n)

= 2.576 * (6.5 / 104)

= 1.6

At 99% confidence interval estimate of the population mean is,

- E < < + E

95.3 - 1.6 < < 95.3+1.6

93.7 < < 96.9

Option b ) is correct.