Q1) Random sample of n = 121 sales invoices was taken from very large population of such  invoices, and average value was found to be $47.50 with sample standard deviation of  $7.50. Determine a 90% confidence interval for mean value of all invoices. Compare this interval with that obtained under simplifying assumption that population standard deviation is equal to sample standard deviation.

Random sample of 10 flights from Amsterdam to Paris yields following flight-times (in minutes):

44 43 44 35 40    

40 39 42 36 37         

Find out a 95% confidence interval for μ, and use this to explain the conjecture that flying from Amsterdam to Paris takes on average 42 minutes. Test this conjecture with formal hypothesis test, by using a 5% significance level. Find out the p-value for hypothesis test.