According to an IRS study, it takes an average of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. A consumer watchdog agency selects a random sample of 40 taxpayers and finds the standard deviation of the time to prepare, copy, and electronically file form 1040 is 80 minutes.
a) What assumption or assumptions do you need to make about the shape of the population?
b) What is the standard error of the mean in this example?
c) What is the likelihood the sample mean is greater than 320 minutes?
d) What is the likelihood the sample mean is between 320 and 350 minutes?
e) What is the likelihood the sample mean is greater than 350 minutes?
a) Since the sample size is normal, the shape of the distribution is "NORMAL"
b) The standard error of the mean is given as
SE = σ / √n
Since the sample size is large, sample standard deviation can be used in place of population standard deviation
SE = s / √n
SE = ...
This solution addresses 5 statistics questions revolving around the sample mean.