14.20

Reading a computer screen. Does the use of fancy type fonts slow down the reading of text on a computer screen?  Adults can read four paragraphs of text in an average time of 22 seconds in the common Times New Roman font.  Ask 25 adults to read this text in the ornate font names Gigi.  Here are their times:

$\begin{array}{rrrrrrrrr} 23.2 & 21.2 & 28.9 & 27.7 & 29.1 & 27.3 & 16.1 & 22.6 & 25.6 \\ 34.4 & 23.9 & 26.8 & 20.5 & 34.3 & 21.4 & 32.6 & 26.2 & 34.1 \\ 31.5 & 24.6 & 23.0 & 28.6 & 24.4 & 28.1 & 41.3 & & \end{array}$

Suppose that the reading times are Normal with $\sigma=6$ seconds.  Is there good evidence that the mean reading time for Gigi is greater than 22 seconds?

Solution

The null hypothesis should read: The mean reading time for Gigi, $\mu$ is not different from the mean reading time for Times New Roman, $\mu_0 = 22.$  The alternative hypothesis claims that the mean reading time for Gigi is greater than that for Times New Roman.  We have then:

$\begin{cases} H_0 &: \mu = 22 \text{ seconds.} \\ H_a &: \mu > 22 \text{ seconds.} \end{cases}$

Under the simple conditions stated in the body of the problem (proper SRS, Normal distribution, standard deviation provided) we are justified to use z statistics. The test statistic in this case is then

$z = \displaystyle{\frac{\bar{x}-\mu_0}{\sigma/\sqrt{n}}},$

where $\sigma = 6$, $\mu_0=22$ and $n=25$ are given directly.  The mean reading times of the SRS, after proper computation gives $\bar{x} = 27.09.$  In this case, the z statistic is $z=4.24166667.$

Notice that this value is not even included in table A.  The corresponding P-value is then very close to zero (and therefore, small enough given any significance threshold $\alpha$).  This is strong evidence against the null hypothesis, and thus we claim that the observed $\bar{x} = 27.09$ is indeed good evidence that reading texts with the font Gigi takes longer than with the font Times New Roman.