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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 α=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×p≥10: n×p=100×0.13=13>10

(b) n×(1-p)≥10: n×(1-p)=100×(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

We want to be rich In a recent year, 73%of first-year college students responding to a national survey identified “being very well-off financially” as an important personal goal. A state university finds that 132of an SRS of 200of its first-year students say that this goal is important. Is there convincing evidence at the α=0.05significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value of 73%?

The reason we use t procedures instead of z procedures when carrying out a test about a population mean is that

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