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Chapter 9: Q R9.4 (page 615)

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):

Do these data provide convincing evidence that it takes adults longer than 22 seconds, on average, to read these four paragraphs in Gigi font?

Short Answer

Expert verified

Yes, there is sufficient evidence to show that reading of four paragraphs requires more than22 seconds.

Step by step solution

01

Step 1:Given information

The data is

02

Step 2:Explaination

The test statistic formula is:

t=x炉-渭osh

Consider, 渭be the average reading time to read the four paragraphs.

The null and alternative hypotheses are:

H0:渭=22

Ha:渭>22

The alternative hypothesis represents that the test is right tailed.

The obtained Minitab output is:

The p-value is0.000.

Here,p-value(0.000)<伪(0.05)

The null hypothesis is rejected.

Therefore,

At5% level of significance there is sufficient evidence to show that reading of four paragraphs requires more than 22seconds.

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Most popular questions from this chapter

You are testing H0:渭=10against Ha:渭<10based on an SRS of20

observations from a Normal population. The t statistic is t=鈭�2.25

The P-value

a. falls between 0.01 and 0.02.

b. falls between 0.02 and 0.04.

c. falls between 0.04 and 0.05.

d. falls between 0.05 and 0.25.

e. is greater than 0.25.

Clean water The Environmental Protection Agency (EPA) has determined that safe

drinking water should contain at most 1.3mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of30randomly selected locations. The company performs a test at the 伪=0.05 significance level ofH0:渭=1.3versus Ha:渭>1.3, where 渭 is the

true mean copper content of the water from the new source.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the company鈥檚 choice of 伪=0.05? Why or why not?

Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a loud noise as stimulus. The appropriate hypotheses for the significance test are

a. H0:渭=18;Ha:渭鈮�18

b. H0:渭=18;Ha:渭>18

c. H0:渭<18;Ha:渭=18

d. H0:渭=18;Ha:渭<18

e. H0:x炉=18;Ha:x炉<18

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

Side effects A drug manufacturer claims that less than 10%of patients who take its new drug for treating Alzheimer鈥檚 disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of 300out of 5000Alzheimer鈥檚 patients whose families have given informed consent for the patients to participate in the study. In all, 25of the subjects experience nausea.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Do these data provide convincing evidence for the drug manufacturer鈥檚 claim?
See all solutions

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