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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:μ1≤μ2Ha:μ1<μ2

The significant level, α=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 15 exercises: Indicate if the hypothesis test is for

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

A sample of 12 in-state graduate school programs at school A has a mean tuition of \(64,000 with a standard deviation of \)8,000. At school B, a sample of 16 in-state graduate programs has a mean of \(80,000 with a standard deviation of \)6,000. On average, are the mean tuitions different?

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Is this a test of means or proportions?
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