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3 years ago

Solve

Mathematics

1 answer:

NISA [10]3 years ago

6 0

Answer:

$r = 0.01$

Step-by-step explanation:

In order to find r we have to square both sides of the equation

$0.1 = \sqrt{r} \\ {0.1}^{2} = { \sqrt{r} }^{2}$

The *square root* sign cancels out the *squared* sign therefore:

${0.1}^{2} = r \\ 0.01 = r$

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And for this case we know that is the best estimator since is an unbiased estimator for the true population mean since we have this:

$E(\bar X) = E(\frac{\sum_{i=1}^n x_i}{n})= \frac{1}{n} \sum_{i=1}^n E(X_i) = \frac{n\mu}{n} = \mu$

Step-by-step explanation:

For this case we have the following values given:

82, 96, 99, 102, 103, 103, 106, 107, 108, 108, 108, 108, 109, 110, 110, 111, 113, 113, 113, 113, 115, 115, 118, 118, 119, 121, 122, 122, 127, 132, 136, 140, 146

And we want to estimate the mean value of IQ for the conceptual population.

For this case we can use as estimator for the population mean the sample mean. We know that the sample mean is given by this formula:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}$

Where n represent the sample size, on this case n =33. If we use this formula we got:

$\bar X = 113.727$

And for this case we know that is the best estimator since is an unbiased estimator for the true population mean since we have this:

$E(\bar X) = E(\frac{\sum_{i=1}^n x_i}{n})= \frac{1}{n} \sum_{i=1}^n E(X_i) = \frac{n\mu}{n} = \mu$

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3 years ago