Question

Reading level A school librarian purchases a novel for her library. The publisher claims that the book is written at a fifth-grade reading level, but the librarian suspects that the reading level is lower than that. The librarian selects a random sample of $40$pages and uses a standard readability test to assess the reading level of each page. The mean reading level of these pages is $4.8$ with a standard deviation of $0.8.$Do these data give convincing

evidence at the $\alpha =0.05$significance level that the average reading level of this novel is less than 5?

Short answer

The required answer is:

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

Step-by-step solution

Given information

Population mean $\left(\mu \right)=5$

sample mean $\left(\overline{x}\right)=4.8$

Sample size $\left(n\right)=40$

Sample standard deviation$\left(s\right)=0.8$

Formula used

We know,

The test statistic formula is:$t=\frac{\overline{x}-{\mu }_o}{\frac{s}{\sqrt{n}}}$

The objective is to find whether there are sufficient evidence to conclude that the average reading level of a novel is less than 5at 5%the significance level.

The null and alternative hypotheses are as follows:

$$\begin{gathered} H_0:\mu =5 \\ {H}_a:\mu <5 \end{gathered}$$

The alternative hypothesis denotes that the test is left-handed.

The Minitab output is as follows:

The $p$-value is $0.029$

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

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