Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

n = 10, x = 12.8, s = 2.8, 95 percent

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 12.8

sample standard deviation = s = 2.8

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,9 = 2.262

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

= 2.262 * ( 2.8 / 10)

Margin of error = E = 2.00

The 95% confidence interval estimate of the population mean is,

  ± E  

= 12.8  ± 2.00

=( 10.80, 14.80 )