Question

A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 16 days revealed average of 200,000 and a sample standard deviation of 18,000. Assume that the sales are believed to be normally distributed. Provide a 90% confident interval for the average daily sales.

Answer 1

Solution :

Given that,

= 200,000

s = 18,000.

n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,15 =1.753

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

= 1.753 * (18,000 / 16 )

=7888.5

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

- E < < + E

200,000 - 7888.5< < 200,000 + 7888.5

192111.5 < <207888.5

(192111.5, 207888.5 )