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Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be \(\sigma=10\) \(\sigma=10\) meters. An experienced jumper thinks that the organizers are underestimating the variation.

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01

Step 1:Given information

Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be $\sigma=10$ $\sigma=10$ meters. An experienced jumper thinks that the organizers are underestimating the variation.

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

02

Step 2:Explaination

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Most popular questions from this chapter

You are testing H0:ฮผ=10against Ha:ฮผ<10based on an SRS of20

observations from a Normal population. The t statistic is t=โˆ’2.25

The P-value

a. falls between 0.01 and 0.02.

b. falls between 0.02 and 0.04.

c. falls between 0.04 and 0.05.

d. falls between 0.05 and 0.25.

e. is greater than 0.25.

After once again losing a football game to the archrival, a collegeโ€™s alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing the coach. Suppose you wish to see if a majority of all living alumni is in favor of firing the coach. The appropriate standardized test statistic is

(a)z=0.64-0.50.64(0.36)100z=0.64-0.50.64(0.36)100

role="math" localid="1654432946823" (b)t=0.64-0.50.64(0.36)100t=0.64-0.50.64(0.36)100

(c)z=0.64-0.50.5(0.5)100z=0.64-0.50.5(0.5)100

(d)z=0.64-0.50.64(0.36)64z=0.64-0.50.64(0.36)64

(e)z=0.5-0.640.5(0.5)100z=0.5-0.640.5(0.5)100

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 isnโ€™t 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.

Attitudes Refer to Exercise 4. In the study of older studentsโ€™ 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.

Fair coin? You want to determine if a coin is fair. So you toss it 10times and record the proportion of tosses that land โ€œheads.โ€ You would like to perform a test of H0:p=0.5versus Ha:pโ‰ 0.5, where p= the proportion of all tosses of the

coin that would land โ€œheads.โ€ Check if the conditions for performing the significance test are met.

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