Q.7 - The Practice of Statistics for AP

Question

 Fonts and reading ease 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 the common Times New Roman font in an average time of $22$ seconds. Researchers asked a random sample of $24$ adults to read this text in the omate font named Gigi. Here are their times, in seconds:

23.2	21.2	28.9	27.7	29.1	27.3	16.1	22.6	25.6	34.2	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

Do these data provide good evidence that the mean reading time for Gigi is greater than  $22$seconds? Carry out an appropriate test to help you answer this question.

- Use a confidence interval to draw a conclusion for a two-sided test about a population mean.

Step-by-Step Solution

Answer

Yes, there is sufficient evidence to conclude that the mean reading time for Gigi is more than $22$ seconds,

Step-1 Given Information

Given in the question that,

23.2	21.2	28.9	27.7	29.1	27.3	16.1	22.6	25.6	34.2	23.9	26.8
20.5	34.3	21.4	32.6	26.2	34.1	31.5	24.6	23	28.6	24.4	28.1

we have to find out that Do these data provide good evidence that the mean reading time for Gigi is greater than  $22$seconds.

Step-2 Explanation

The formula used to compute the test statistic is:

$t=\frac{\overline{x}-\mu }{{\displaystyle \frac{s}{\sqrt{n}}}}$

The null and alternative hypothesis are:

$H_0:\mu =22$

$H_{\alpha }:\mu >22$

Assume level of significance to be $0.05$

the obtained output is:

The significance level is less than the$p-value(0.000)$ in this case. As a result, the null hypothesis is ruled out. As a result, there is enough information to indicate that Gigi's average reading time is greater than $22$ seconds.