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Chapter 9: Q. 75 (page 607)

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 4.8with 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?

Short Answer

Expert verified

No, there is insufficient evidence to conclude that average reading level of novel is less than5.

Step by step solution

01

Step 1. Given information

Population on mean (μ)=5

Standard mean(x¯)=4.8

Sample size(n)=40

Sample standard deviation(s)=0.8

02

Step 2. Explanation

The null and alternative hypotheses are:

H0:μ=5Ha:μ<5

The alternative hypothesis represents that the test is left tailed.

The obtained Minitab output is:

The p-value is 0.029

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

At 5%level of significance there is insufficient evidence to conclude that average reading level of novel is less than5.

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Most popular questions from this chapter

A government report says that the average amount of money spent per U.S. household per week on food is about \(158. A random sample of50 households in a small city is selected, and their weekly spending on food is recorded. The sample data have a mean of \)165 and a standard deviation of \(20. Is there convincing evidence that the mean weekly spending on food in this city differs from the national figure of \)158?

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a. Define the parameter of interest.

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d. Do these data give convincing evidence that the actual population proportion differs from 0.5? Justify your answer with appropriate evidence.

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.13

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Interpreting a P-value A student performs a test of H0:p=0.3H0:p=0.3versus Ha:p<0.3Ha:p<0.3and gets a P-value of 0.22The student says, "This means there is about a22%chance that the null hypothesis is true." Explain why the student's explanation is wrong.

Fonts and reading ease Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can read four paragraphs of a certain text in the common Times New Roman font in an average time of 22 seconds. Researchers asked a random sample of 24 adults to read this text in the ornate font named Gigi. Here are their times (in seconds):

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