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GarryVolchara [31]
3 years ago
6

Each year, all final year students take a mathematics exam. It is hypothesised that the population mean score for this test is 8

0. 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.
Mathematics
1 answer:
VMariaS [17]3 years ago
7 0

Answer:

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

Step-by-step explanation:

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

\alpha = \frac{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\frac{\sigma}{\sqrt{n}}

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

M = 1.645\frac{13}{\sqrt{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.

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