Question

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). In an initial study, eight runs were made. The average flow rate was 6.4 gpm and the standard deviation was 1.9 gpm. If the mean flow rate is found to meet the specification, the pump will be put into service.
1. State the appropriate null and alternate hypotheses.
2. Find the P-value.
3. Should the pump be put into service? Explain.

Answer 1

Answer:

1.

The null hypothesis is $H_0: \mu = 4$

The alternate hypothesis is $H_1: \mu > 4$

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:

$H_0: \mu = 4$

At the alternate hypothesis, we test that the mean is more than 4, that is:

$H_1: \mu > 4$

The test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ 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 $\mu = 4$

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 $n = 8, X = 6.4, s = 1.9$

Test statistic:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{6.4 - 4}{\frac{1.9}{\sqrt{8}}}$

$t = 3.57$

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.