Question

A random sample of size 17 Yields x=3.49 and s^2=1.53. Complete parts A thru E Below.

a. Calculate a confidence interval for the population mean whose confidence level is 0.99.

b. Calculate a confidence interval for the population mean whose confidence level is 0.98.

c. Calculate a confidence interval for the population mean whose confidence level is 0.95.

d. Calculate a confidence interval for the population mean whose confidence level is 0.90.

e. Calculate a confidence interval for the population mean whose confidence level is 0.80.

Answer 1

Given sample size n = 17

mean = 3.49 , sample variance s² = 1.53 => sample standard deviation s = sqrt(1.53) = 1.24

We have to use t-distribution for this because population variance is unknown.

Confidence Interval CI =

alpha = 1 - 0.01*confidence

a. Calculate a confidence interval for the population mean whose confidence level is 0.99.

alpha = 0.01

Critical value = t_0.005,16 = 2.921

by substituting all values we get 99% CI = (2.614 , 4.366)

b) alpha = 0.02 , Critical value = t_0.01,16 = 2.583

by substituting all values we get 98% CI = (2.715 , 4.265)

c) alpha = 0.05 , Critical value = t_0.025,16 = 2.120

by substituting all values we get 95% CI = (2.854 , 4.126)

d) alpha = 0.10 , Critical value = t_0.05,16 = 1.746

by substituting all values we get 90% CI = (2.966 , 4.014)

e) alpha = 0.20 , Critical value = t_0.10,16 = 1.337

by substituting all values we get 80% CI = (3.089 , 3.891)