Respuesta :
Answer:
1.
The null hypothesis is [tex]H_0: \mu = 4[/tex]
The alternate hypothesis is [tex]H_1: \mu > 4[/tex]
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:
[tex]H_0: \mu = 4[/tex]
At the alternate hypothesis, we test that the mean is more than 4, that is:
[tex]H_1: \mu > 4[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] 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 [tex]\mu = 4[/tex]
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 [tex]n = 8, X = 6.4, s = 1.9[/tex]
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{6.4 - 4}{\frac{1.9}{\sqrt{8}}}[/tex]
[tex]t = 3.57[/tex]
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.
