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Chapter 9: Q T9.1 (page 616)

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

邪.H0:p鈭�=0.5;Ha:p鈭�>0.5H0:p^=0.5;Ha:p^>0.5.

b. H0:p=0.5;Ha:p>0.5H0:p=0.5;Ha:p>0.5.

c. H0:p=0.5;Ha:p<0.5H0:p=0.5;Ha:p<0.5.

d. H0:p=0.5;Ha:p鈮�0.H0:p=0.5;Ha:p鈮�0.5.

e. H0:p>0.5;Ha:p=0.5H0:p>0.5;Ha:p=0.5.

Short Answer

Expert verified

So, the correct answer is option (b) that isH0:p=0.5,Ha:p>0.5.

Step by step solution

01

Step 1:Given information

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban

02

Step 2:Explaination

The hypotheses are statements about the population parameter:

p: Population parameter.

渭:Population mean.

蟽: Population standard deviation.

The null hypothesis states that the population parameter is equal to the value mentioned in the claim:

H0:p=50%=0.50

The alternative hypothesis states the opposite of the null hypothesis (according to the claim):

Ha:p>0.50

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Most popular questions from this chapter

How much juice? Refer to Exercises 3 and 11 .

a. What conclusion would you make at the 伪=0.10伪=0.10level?

b. Would your conclusion from part (a) change if a 5 \% significance level was used instead? Explain your reasoning.

Attitudes Refer to Exercise 4. In the study of older students鈥� attitudes, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101.

a. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.

Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1% increase in the sales tax to fund road repairs.

A Type I error in the context of this study occurs if the city council

a. finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn鈥檛 convincing evidence that a majority supports the increase.

b. finds convincing evidence that a majority of residents supports the tax increase, when in reality at most 50%of city residents support the increase.

c. finds convincing evidence that a majority of residents supports the tax increase, when in reality more than 50%of city residents do support the increase.

d. does not find convincing evidence that a majority of residents supports the tax increase, when in reality more than 50%of city residents do support the increase.

You are testing H0:渭=10 against Ha:渭鈮�10 based on an SRS of 15

observations from a Normal population. What values of the t statistic are statistically significant at the 伪=0.005 level?

a.t>3.326b.t>3.286c.t>2.977d.t<鈭�3.326ort>3.326e.t<鈭�3.286ort>3.286

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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