Question

A random sample of 10 males from a normal population showed a mean height 66
inches and the sum of squares from this mean is equal to 90 sq inches. Is it
reasonable to believe that the average height is greater than 64 inches. Justify your
answer.

Answer 1

Answer on Question #54877 – Math – Statistics and Probability

A random sample of $n = 10$ males from a normal population showed a mean height $\bar{x} = 66$ inches and the sum of squares from this mean is equal to $SSX = 90$ sq. inches. Is it reasonable to believe that the average height is greater than 64 inches? Justify your answer.

Solution

The standard deviation is

$$s = \sqrt{\frac{SSX}{n - 1}} = \sqrt{\frac{90}{10 - 1}} = \sqrt{10}.$$ $$\begin{array}{l} P(\mu > 64) = P\left(z > \frac{64 - \bar{x}}{\frac{s}{\sqrt{n}}}\right) = P\left(z > \frac{64 - 66}{\frac{\sqrt{10}}{\sqrt{10}}}\right) = P(z > -2) = 1 - P(z < -2) = 1 - 0.0228 \\ = 0.9772. \end{array}$$

It is reasonable to believe that the average height is greater than 64 inches, because the chance of this event is $97.72\%$.

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