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2 answers:
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Answer:
1.
The null hypothesis is
The alternate hypothesis is
2.
The p-value of the test is of 0.0045.
3.
The p-value of the test is low(< 0.01), which means that there is enough evidence that the flow rate is more than 4 gallons per minute (gpm) and thus, the pump should be put into service.
Step-by-step explanation:
A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the flow rate be more than 4 gallons per minute (gpm).
At the null hypothesis, we test that the mean is 4, so:
At the alternate hypothesis, we test that the mean is more than 4, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
4 is tested at the null hypothesis:
This means that
In an initial study, eight runs were made. The average flow rate was 6.4 gpm and the standard deviation was 1.9 gpm.
This means that
Test statistic:
P-value of the test:
The p-value of the test is the probability of finding a sample mean above 6.4, which is a right-tailed test with t = 3.57 and 8 - 1 = 7 degrees of freedom.
With the help of a calculator, the p-value of the test is of 0.0045.
3. Should the pump be put into service?
The p-value of the test is low(< 0.01), which means that there is enough evidence that the flow rate is more than 4 gallons per minute (gpm) and thus, the pump should be put into service.
Answer:
x ≈ 26.4
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos47° = =
=
( multiply both sides by x )
x × cos47° = 18 ( divide both sides by cos47° )
x = ≈ 26.4 ( to the nearest tenth )