Problem 3

A simple random sample of size nine is drawn from a population of 6000 high school students. The students in the sample are administered IQ tests; the other students are not. The IQs of the students in the sample are:

- 133.23
- 98.2
- 106.92
- 102.38
- 104.05
- 99.74
- 63.31
- 112.65
- 103.11

Determine the following:

1. The sample mean of the IQ scores is (Q8).
2. The sample standard deviation of the IQ scores is (Q11).
3. The finite population correction is (Q13).
4. The estimated standard error of the sample mean of the IQ scores is (Q14).

This mathematical problem involves calculating various statistics from a simple random sample of IQ scores of high school students. These statistics include the sample mean, sample standard deviation, finite population correction, and estimated standard error of the sample mean.

Explanation:

In the given task, we are analyzing IQ test scores of a sample of high school students. This data consists of a simple random sample of nine students from a population of 6000. To perform this analysis, we need to calculate the sample mean (Q8), sample standard deviation (Q11), finite population correction (Q13), and the estimated standard error of the sample mean (Q14). The sample mean of IQ scores is the total sum of all the scores divided by the number of scores. Similarly, the sample standard deviation is a measure of the amount of variation or dispersion of the set of values. The finite population correction is applied when sampling is done without replacement from a finite population size, usually when the sample size is more than 5% of the population. Finally, the estimated standard error of the sample mean indicates the variation in the sample mean if you were to perform the sampling over and over again.

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