Question

A random sample of workers have been surveyed and data collected on how long it takes them to travel to work. The data are in this file.

1. Compute a 99% confidence interval for the expected time taken to travel to work. Show all your working and state any assumptions you need to make in order for your confidence interval to be valid.
2. Interpret the confidence interval

x
46.13229
43.06446
42.52708
42.12789
44.92402
34.43817
41.85524
44.2512
50.86619
34.34349
50.98036

Answer 1

The following table will be used to make the computations here:

X	(X - Mean(X))	(X - Mean(X))^2
46.13229	2.904072727	8.433638405
43.06446	-0.163757273	0.026816444
42.52708	-0.701137273	0.491593475
42.12789	-1.100327273	1.210720107
44.92402	1.695802727	2.87574689
34.43817	-8.790047273	77.26493106
41.85524	-1.372977273	1.885066591
44.2512	1.022982727	1.04649366
50.86619	7.637972727	58.33862738
34.34349	-8.884727273	78.93837871
50.98036	7.752142727	60.09571686
475.5104		290.6077296

The sample mean here is computed as:

For n - 1 = 10 degrees of freedom, we get from the t distribution tables here:

P( t10 < 3.169) = 0.995

Therefore, due to symmetry, we get here:
P( -3.169 < t10 < 3.169) = 0.99

Therefore the confidence interval here is obtained as:

This is the required 99% confidence interval for the population mean.

The interpretation of the confidence interval here is that there is a 99% probability that the true population mean lies in the given interval.