Chapter 9.3, Problem 75E

To determine

To find: Whether there are sufficient evidence to conclude that average reading level of novel is less than 5 at 5% significance level.

Answer to Problem 75E

No, there is insufficient evidence to conclude that average reading level of novel is less than 5.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Population mean}\left(\mu \right)=5\\ \text{Sample mean}\left(\overline{x}\right)=4.8\\ \text{Sample size}\left(n\right)=40\\ \text{Sample standard deviation}\left(s\right)=0.8\end{array}$

Formula used:

The test statistic formula is:

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

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =5\\ H_a:\mu <5\end{array}$

The alternative hypothesis represents that the test is left tailed.

The obtained Minitab output is:

  

The p -value is 0.029.

Here, $p\text{-value}\left(0.061\right)>\alpha \left(0.05\right)$ . The null hypothesis is not rejected.

Conclusion:

At 5% level of significance there is insufficient evidence to conclude that average reading level of novel is less than 5.