Question

In a recent sample of 83 used cars sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) a.) Construct a 95% confidence interval for the population mean cost of a used car. b.)(iii) Calculate the error bound. (Round your answer to one decimal place.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 6425

sample standard deviation = s = 3156

sample size = n = 83

Degrees of freedom = df = n - 1 = 83 - 1 = 82

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,82 = 1.989

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

= 1.989 * ( 3156/ 83)

Margin of error = E = 689.0

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

  ± E  

= 6425  ± 689.0

= ( $ 5736.0, $ 7114.0 )

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

= 1.989 * ( 3156/ 83)

Margin of error = E = 689.0