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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 伪=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 (渭)=5

Standard mean(x炉)=4.8

Sample size(n)=40

Sample standard deviation(s)=0.8

02

Step 2. Explanation

The null and alternative hypotheses are:

H0:渭=5Ha:渭<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)>伪(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

Which of the following 95%confidence intervals would lead us to reject H0:p=0.30in favor of Ha:pnotequalto0.30at the 5%significance level?

a. (0.19,0.27)

b.(0.24,0.30)

c. (0.27,0.31)

d. (0.29,0.31)

e. None of these

Roulette An American roulette wheel has 18red slots among its 38slots. To test if a particular roulette wheel is fair, you spin the wheel 50times and the ball lands in a red slot 31times. The resulting P-value is0.0384.

a. Interpret the P-value.

b. What conclusion would you make at the伪=0.05 level?

c. The casino manager uses your data to produce a99% confidence interval for p and gets(0.44,0.80). He says that this interval provides convincing evidence that the wheel is fair. How do you respond

Restaurant power Refer to Exercise 86 Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.

a. Use a random sample of 30 people instead of 50 people.

b. Try to detect that 渭=\(85,500 instead of 渭=\)86,000

c. Change the significance level to 伪=0.10

Making conclusions A student performs a test of H0:p=0.75versus Ha:p<0.75at 伪=0.05significance level and gets a P-value of 0.22

The student writes: 鈥淏ecause the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at a local high school. Before the change, 37%of students approve of the parking that's provided. The null hypothesis H0:p>0.37H0:p>0.37is tested against the alternative Ha: p=0.37Ha:p=0.37

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

H0:x-=3000grams-5H0:x炉=3000grams

Ha: x-<3000grams Ha:x炉<3000grams

explain what's wrong with the stated hypotheses. Then give correct hypotheses.
See all solutions

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