Question

As part of an annual review of its accounts, a discount brokerage selects a random sample of 27 customers. Their accounts are reviewed for total account valuation, which showed a mean of $32,500, with a sample standard deviation of $8,600. (Use t Distribution Table.)

What is a 95% confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount.)

95% confidence interval for the mean account valuation is between $  and $  .

Answer 1

Solution :

Given that,

= $32,500

s =  $8,600

n = 27

Degrees of freedom = df = n - 1 = 27 - 1 = 26

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,26 =2.056

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

= 2.056 * (8600 / 27) = 3403

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

- E < < + E

32500 - 3403 < < 32500 + 3403

29097 < < 35903

(29097 ,  35903)

answer =$29097 and $35903