Question

Construct the indicated confidence interval for the population mean mu using the​ t-distribution. Assume the population is normally distributed. cequals0.90​, x overbarequals13.9​, sequals3.0​, nequals6 The 90​% confidence interval using a​ t-distribution is left parenthesis nothing comma nothing right parenthesis.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 13.9

sample standard deviation = s = 3.0

sample size = n = 6

Degrees of freedom = df = n - 1 = 6 - 1 = 5

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t_0.05,5 = 2.015

Margin of error = E = t_/2,df * (s /n)

= 2.015 * ( 3.0 / 6)

Margin of error = E = 2.47

The 90% confidence interval estimate of the population mean is,

  ± E

= 13.9  ± 2.47

= ( 11.43, 16.37 )