Question

A random sample of workers have been surveyed and data collected on how long it takes them to travel to work. The data in the table below.

x

46.1322892

43.06446333

42.52707962

42.12788557

44.924022

34.43816828

41.85523528

44.25119865

50.8661868

34.34349438

50.9803572

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.

Answer 1

The assumption: 1) This data is taken from a normal population.

2) This sample is a random sample of the population.

Here mean of the data is: 43.22822 and the sample standard deviation is 5.390803

Now as the population is normal and population standard deviation is not given we'll be using t-distribution with n-1=10 degrees of freedom. The 99% confidence interval of the expected mean is given by:

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