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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

Losing weight A Gallup poll found that 59% of the people in its sample said 鈥淵es鈥� when asked, 鈥淲ould you like to lose weight?鈥� Gallup announced: 鈥淔or results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 卤3 卤3percentage points.鈥�12 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they want to lose weight differs from 0.55? Explain your reasoning

A significance test allows you to reject a null hypothesis H0H0in favor of an alternative hypothesisHaaat the 5%significance level. What can you say about significance at the1%level?

a.H0H0can be rejected at the1%significance level.

b. There is insufficient evidence to rejectH0H0at the1%significance level.

c. There is sufficient evidence to accept H0H0at the 1%significance level.

d.HaHacan be rejected at the 1%significance level.

e. The answer can't be determined from the information given.

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.

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

Pressing pills Refer to Exercise 77.

a. Construct and interpret a 95% confidence interval for the true hardness 渭 of the tablets in this batch. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 77.
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