Question

If n = 22 , overline x (x-bar)=41 , and s = 9 , construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population Give your answers to one decimal place

Answer 1

Confidence interval is written as

point estimate ± margin of error

In this scenario, point estimate is the sample mean.

From the information given,

sample mean = 41

sample standard deviation, s = 9

sample size = 22

Since the population standard deviation is unknown, we would calculate the margin of error by applying the formula,

margin of error = t x s/√n

where

t is the test score for the 80% confidence. It is gotten from the student's t distribution table. To find t, the first step is to find the degree of freedom, df

df = n - 1 = 22 - 1

df = 21

From the table,

t = 1.323

margin of error = 1.323 x 9/√22

margin of error = 2.53858

Confidence interval is

41 ± 2.5

Lower limit = 41 - 2.5 = 38.5

Upper limit = 41 + 2.5 = 43.5

Thus, the final answer is

38.5 < μ < 43.5