Question

A random sample of n = 64 observations has a mean x = 29.9 and a standard deviation s = 3.7.

(a) Give the point estimate of the population mean μ. Find the 95% margin of error for your estimate. (Round your answer to four decimal places.)
(b) Find a 90% confidence interval for μ. (Round your answers to three decimal places.)

Answer 1

(29.128,30.672)

Explanation:

Given that a random sample of n = 64 observations has a mean x = 29.9 and a standard deviation s = 3.7.

a) the point estimate of the population mean μ.

= Sample mean = 29.9

For 90% we use t critical value since population standard deviation is not known.

T critical for 90% is 1.669

Margin of error = ±
`1.669*\sqrt{(3.7)/(√(64) ) } \\=0.7719`

b) Confidence interval 90%

= Mean±Marginof error

=
`(29.128,30.672)`