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1. An intelligence quotient, or IQ, is a measurement of intelligence derived from a standardized test...

1. An intelligence quotient, or IQ, is a measurement of intelligence derived from a standardized test such as the Stanford Binet IQ test. Scores on the test are normal distribution with a mean score of 100 and a standard deviation of 15.

  1. Draw 1000 samples of size n=9 from the distribution of IQ. Calculate the sample mean of all 1000 samples.

  2. Draw the histogram for all sample means in. What is the shape of the sample means?

  3. Calculate mean of all sample means and standard deviation. Compare them with the population mean and standard deviation.

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Answer #1

Means and standard deviations of samples od size 9.

We draw 1000 samples of size n=9 from the distribution of IQ which follows mean 100 and standard deviation 15. The histogram of the sample means of all 1000 samples is giving below

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The shape of the histogram of the sample means is symmetric and the mean, median, and mode of the means fall near to the value 100.

The calculated mean of all sample means and standard deviations are 99.937 and 14.467 respectively. So, these two values are approximately the same with the given mean score of 100 and a standard deviation of 15.

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