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Chapter 9: Q 40. (page 581)

Walking to school Refer to Exercise 36.

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?

Short Answer

Expert verified

a. Sample proportion of 0.17<0.13.

b. Z=1.19,P=0.1170

c. No enough convincing evidence is present that true population proportion of all students at elementary school who walk is>0.13

Step by step solution

01

Given Information

It is given that 伪=0.05

H0:p=0.13

H1:p>0.13

n=100,x=17

02

Explaining Sample Results

The sample proportion is:

p^=xn=17100=0.17

As 0.17>0.13, sample result gives some evidence for alternate hypothesis as it agrees with it.

Hence,H1:p>0.17

03

Standardized test statistic and P value

As sample proportion is 0.17

Test statistic is z=p^-p0p01-p0n=0.17-0.130.13(1-0.13)100=1.19

Pvalue is P=P(z>1.19)=1-P(Z<1.19)=1-0.8830

P=0.1170

04

Conclusion

We get

P=P(z>1.19)=1-P(Z<1.19)=1-0.8830=0.1170

Now, P>0.05鈬�Fail to rejectH0

Hence, there is no enough convincing evidence that true population of all students>0.13

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