Question

A random sample of workers have been surveyed and data collected on how long it takes...

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.
Math   Statistics-And-Probability   
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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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