Question

LeftiesThere have been several studies conducted in an attempt to identify ways in whichleft-handed people are different from those who are right handed. Assume that you want toestimate the mean IQ of all left-handed adults. How many random left-handed adults mustbe tested in order to be 99% confident that the mean IQ of the sample group is within four IQpoints of the mean IQ of all left-handed adults? Assume that \(\sigma \) 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 adultsis 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 ofsignificance 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 adultsis computed as follows:

\[\begin{array}{c}n = \frac{{{{\left( {{z_{\frac{\alpha }{2}}} \times \sigma } \right)}^2}}}{{{E^2}}}\\ = \frac{{{{2.5758}^2} \times {{15}^2}}}{{{4^2}}}\\ = 93.301\\ \approx 94\end{array}\]

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