Question

The average stock prices of 20 technology companies were compared to see whether they improved one year after the 2008 stock market crash (2008 – 2009). The mean of the differences was computed to be –17.8 USD with a standard deviation of 4.81 USD. Calculate and interpret a 95% confidence interval for the average change in stock prices over the two years.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = -17.8

sample standard deviation = s = 4.81

sample size = n = 20

Degrees of freedom = df = n - 1 = 19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,19 = 2.093

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

= 2.093 * (4.81 / 20)

= 2.251

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

- E < < + E

-17.8 - 2.251 < < -17.8 + 2.251

-20.1 < < -15.5

(-20.1 , -15.5)

Therefore, there is 95% confident that the average change in stock prices over the two years is between -20.1 to -15.5.