Chapter 9: Q. 75. (page 607)

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 $α = 0.05$ significance level that the average reading level of this novel is less than 5?

Expert verified

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

Population mean $(μ) = 5$

sample mean $(\bar{x}) = 4.8$

Sample size $(n) = 40$

Sample standard deviation $(s) = 0.8$

We know,

The test statistic formula is: $t = \frac{\bar{x} - μ_{o}}{\frac{s}{\sqrt{n}}}$

The null and alternative hypotheses are as follows:

$H_{0} : μ = 5 H_{a} : μ < 5$

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 $(0.061) > α (0.05)$ 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 $5 .$

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