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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

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.

Home computersRefer to Exercise 35.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

Home computers Jason reads a report that says 80%of U.S. high school

students have a computer at home. He believes the proportion is smaller than 0.80at his large rural high school. Jason chooses an SRS of 60students and finds that 41have a computer at home. He would like to carry out a test at the 伪=0.05significance level of H0:p=0.80versus Ha:p<0.80, where p= the true

proportion of all students at Jason鈥檚 high school who have a computer at home. Check if the conditions for performing the significance test are met.

Packaging DVDs (6.2,5.3) A manufacturer of digital video discs (DVDs) wants to be sure that the DVDs will fit inside the plastic cases used as packaging. Both the cases and the DVDs are circular. According to the supplier, the diameters of the plastic cases vary Normally with mean 渭=5.3inches and standard deviation 蟽=0.01inch. The DVD manufacturer produces DVDs with mean diameter渭=5.26inches. Their diameters follow a Normal distribution with 蟽=0.02inch.

a. Let X = the diameter of a randomly selected case and Y = the diameter of a randomly selected DVD. Describe the shape, center, and variability of the distribution of the random variable X鈭扽. What is the importance of this random variable to the DVD manufacturer?

b. Calculate the probability that a randomly selected DVD will fit inside a randomly selected case.

c. The production process runs in batches of 100 DVDs. If each of these DVDs is paired with a randomly chosen plastic case, find the probability that all the DVDs fit in their cases.

Philly fanatics? Nationally, the proportion of red cars on the road is 0.12.A statistically minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars. One day during a home game, he takes a random sample of 210cars parked at Citizens Bank Park (the Phillies home field), and counts 35red cars.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in (a) is 0.0187. Interpret the P-value.

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