Question

LeftiesThere have been several studies conducted in an attempt to identify ways in which left-handed people are different from those who are right handed. Assume that you want to estimate the mean IQ of all left-handed adults. How many random left-handed adults must be tested in order to be 99% confident that the mean IQ of the sample group is within four IQ points of the mean IQ of all left-handed adults? Assume that is known to be 15.

Short answer

The number of left-handed adults that must be tested in order to be 99% confident that the mean IQ of the sample group is within four IQ points of the mean IQ of all left-handed adults is 94.

Step-by-step solution

Given information

The level of confidence is 99%.

The margin of error is $E=4$.

The population standard deviation is $\sigma =15$.

Compute the sample size

The level of confidence is 99%, which implies that the level of significance is 0.01.

From the Z table, the critical value at 0.01 level of significance is 2.5758.

The number of left-handed adults that must be tested in order to be 99% confidentthat the mean IQ of the sample group is within four IQ points of the mean IQ of all left-handed adults is computed as follows:

$$\begin{gathered} \mathit{n}\mathbf{=}\frac{{\left(z_{\frac{\alpha }{2}}\times \sigma \right)}^{\mathbf{2}}}{{\mathbf{E}}^{\mathbf{2}}} \\ =\frac{{2.5758}^2\times {15}^2}{4^2} \\ =93.301 \\ \approx 94 \end{gathered}$$

Therefore, the number ofleft-handed adults that must be tested is 94.