Question

TradeLine, is an online stock trading service. To estimate the average number of trades made last month by TradeLine’s clients, you take a simple random sample of 16 clients and find the average number of trades in the sample is 45.8. Since you do not know the population standard deviation, you calculate the sample standard deviation as 12.3. Assume that the population is normally distributed. Show the appropriate 99% confidence interval for the average number of trades for all of TradeLine’s clients.

Answer 1

The confidence interval for a normal distribution is calculated as:

The formula for estimation is:

μ = M ± t(s_M)

where:

M = sample mean
t = t statistic determined by confidence level and degree of freedom =n-1
s_M = standard error = √(s²/n)

Since population standard deviation is unknown hence T -distribution is used for confidence interval calculation.

M = 45.8

df= n-1=16-1 =15
t = 2.95 it is calculated using excel formula =T.INV.2T(0.01,15)
s_M = √(12.3²/16) = 3.08

μ = M ± t(s_M)
μ = 45.8 ± 2.95*3.08
μ = 45.8 ± 9.061

Result

M = 45.8, 99% CI [36.739, 54.861].

So the appropriate 99% confidence interval for the average number of trades for all of TradeLine’s clients is [36.739, 54.861].