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Chapter 10: Q. 10.6 (page 578)

The means of the number of revolutions per minute of two competing engines are to be compared. Thirty engines are randomly assigned to be tested. Both populations have normal distributions. Table given below shows the result. Do the data indicate that Engine 2 has higher RPM than Engine 1? Test at a 5%level of significance.

EngineSample mean number of RPMPopulation Standard Deviation
1150050
2160060

Short Answer

Expert verified

There is sufficient evidence to conclude that the Engine 2runs at a higher RPM than Engine 1.

Step by step solution

01

Given information

The given table shows two samples:

EngineSample Mean Number Of RPMPopulation Sample standard deviation
1150050
2160060

The mean of the number of revolutions per minute of two competing engines is to be compared. Thirty engines are randomly assigned to be tested. Both populations have a normal distribution. Test at a 5%level of significance.

02

Calculation

The null hypothesis is

H0:渭1鈮�渭2Ha:渭1<渭2

The significant level, 伪=5%=0.05..

The p-value is almost zero, so we reject the null hypothesis.

Hence, there is sufficient evidence to conclude that Engine 2runs at a higher RPM than Engine1.

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Most popular questions from this chapter

Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different

baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have

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State the null and alternative hypotheses.

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effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects

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Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1%significance level.

State the null and alternative hypotheses.

Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. Table 10.18 shows the result. Scouters believe that Rodriguez pitches a speedier fastball.

At the 1 % significance level, what is your conclusion?

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Which distribution (normal or Student's t) would you use for this hypothesis test?
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