Question

Use the t-distribution to find a confidence interval for a mean given the relevant sample results. Give the best point estimate for , the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for using the sample results , , and Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.

point estimate = ?
margin of error = ?
The 95% confidence interval is ____ to ______.

Answer 1

Answer: hello your question is incomplete attached below is the complete question

answer :

a) 85.0

b) 27.4

c) (82.26, 87.74 )

Explanation:

Given data :

95% confidence interval

x ( mean ) = 85

s = 8.8

n ( sample size ) = 42

using t-distribution

a) calculate the point estimate

The point estimate = 85.0 given that a sample mean is the same as a point estimate of the sample population

b) calculate the Margin of error

df = 42 - 1 = 41

∝ = 0.05

critical value ( T ∝/2 , 41 ) = 2.02

hence ; margin of error ( E )

= 2.74 ( using margin of error calculator )

c) The 95% confidence interval

= 85 ± 2.74

(82.26, 87.74 )