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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 40pages 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 伪=0.05significance level that the average reading level of this novel is less than 5?

Short Answer

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

01

Given information

Population mean (渭)=5

sample mean (x炉)=4.8

Sample size (n)=40

Sample standard deviation(s)=0.8

02

Formula used

We know,

The test statistic formula is:t=x炉-渭osn

03

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:

H0:渭=5Ha:渭<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)>伪(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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Most popular questions from this chapter

Two-sided test Suppose you want to perform a test of H0:渭=64

versus Ha:渭notequalto64at the 伪=0.05significance level. A random sample

of size n=25 from the population of interest yields x炉=62.8 and sx=5.36

. Assume that the conditions for carrying out the test are met.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be \(\sigma=10\) \(\sigma=10\) meters. An experienced jumper thinks that the organizers are underestimating the variation.

pg559炉

No homework Refer to Exercises 1 and 9. What conclusion would you make at the伪=0.05伪=0.05level?

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

邪.H0:p鈭�=0.5;Ha:p鈭�>0.5H0:p^=0.5;Ha:p^>0.5.

b. H0:p=0.5;Ha:p>0.5H0:p=0.5;Ha:p>0.5.

c. H0:p=0.5;Ha:p<0.5H0:p=0.5;Ha:p<0.5.

d. H0:p=0.5;Ha:p鈮�0.H0:p=0.5;Ha:p鈮�0.5.

e. H0:p>0.5;Ha:p=0.5H0:p>0.5;Ha:p=0.5.

In a test ofH0:p=0.4against Ha:p鈮�0.4, a random sample of size 100 yields a standardized test statistic of z=1.28. Which of the following is closest to the P-value for this test?

a. 0.90

b. 0.40

c. 0.05

d. 0.20

e. 0.10
See all solutions

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