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Chapter 9: Q 36. (page 581)

Walking to school A recent report claimed that 13%of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13at her large elementary school. She surveys a random sample of 100students and finds that 17typically walk to school. DeAnna would like to carry out a test at the 伪=0.05significance level of H0:p=0.13versus Ha:p>0.13, where p= the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

Short Answer

Expert verified

The conditions are fulfilled.

Step by step solution

01

Given Information

It is given that n=100

p=0.13

The null and alternate hypothesis are

H0:p=0.13

Ha:p>0.13

p proportion of students that walk to schools.

02

Checking conditions for significance test

The conditions to be fulfilled are:

(a) n脳p鈮�10: n脳p=100脳0.13=13>10

(b) n脳(1-p)鈮�10: n脳(1-p)=100脳(1-0.13)=870>10

Since both conditions re fulfilled, significance test can be performed.

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Most popular questions from this chapter

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?

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by

a. using only volunteers from the basketball team in the experiment.

b. using伪=0.05 instead of 伪=0.05

c. using 伪=0.05instead of 伪=0.01

d. giving the drug to 25 randomly selected students instead of 50.

e. using a two-sided test instead of a one-sided test.

Which of the following has the greatest probability?

a.P(t>2)if t has 5 degrees of freedom.

b. P(t>2) if t has 2 degrees of freedom.

c. P(z>2) if z is a standard Normal random variable.

d.P(t<2)if t has 5 degrees of freedom.

e.P(z<2) if z is a standard Normal random variable.

Making conclusions A student performs a test of H0:渭=12versus Ha:渭鈮�12

at the 伪=0.05significance level and gets a P-value of 0.01. The

student writes: 鈥淏ecause the P-value is small, we reject H0. The data prove that Hais true.鈥� Explain what is wrong with this conclusion.

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.
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