Chapter 9, Problem R9.4RE

To determine

To find: Whether there are sufficient evidence to show that reading of four paragraphs requires more than 22 seconds.

Answer to Problem R9.4RE

Yes, there is sufficient evidence to show that reading of four paragraphs requires more than 22 seconds.

Explanation of Solution

Given:

The data set is:

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
28.6
24.4
28.1

Formula used:

The test statistic formula is:

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

Calculation:

Consider, µ be the average reading time to read the four paragraphs.

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =22\\ H_a:\mu >22\end{array}$

The alternative hypothesis represents that the test is right tailed.

The obtained Minitab output is:

  

The p -value is 0.000.

Here, $p\text{-value}\left(0.000\right)<\alpha \left(0.05\right)$ . The null hypothesis is rejected.

Conclusion:

At 5% level of significance there is sufficient evidence to show that reading of four paragraphs requires more than 22 seconds.