Question

Each year, all final year students take a mathematics exam. It is hypothesised that the population mean score for this test is 80. It is known that the population standard deviation of test scores is 13. A random sample of 23 students take the exam. The mean score for this group is 71. a)Calculate the 90% confidence interval for the population mean test score. Give your answers to 2 decimal places.

Answer 1

The 90% confidence interval for the population mean test score is between 66.54 and 75.46.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1 - 0.9)/(2) = 0.05`

Now, we have to find z in the Ztable as such z has a pvalue of
`1 - \alpha`.

That is z with a pvalue of
`1 - 0.05 = 0.95`, so Z = 1.645.

Now, find the margin of error M as such

`M = z(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

`M = 1.645(13)/(√(23)) = 4.46`

The lower end of the interval is the sample mean subtracted by M. So it is 71 - 4.46 = 66.54

The upper end of the interval is the sample mean added to M. So it is 71 + 4.46 = 75.46

The 90% confidence interval for the population mean test score is between 66.54 and 75.46.