Question
In: Statistics and Probability
The average stock prices of 20 technology companies were compared to see whether they improved one...
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.
Solutions
Expert Solution
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 = t0.025,19 = 2.093
Margin of error = E = t/2,df
* (s /
= 2.093 * (4.81 /
= 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.
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