A new centrifugal pump is being considered for an applicatio

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 5 gallons per minute (gpm). In an initial study, eight runs were made. The average flow rate was 6.5gpm 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.

Solution

1. State the appropriate null and alternate hypotheses

Let mu be the population mean

Null hypothesis: mu=5

Alternative hypothesis: mu>5

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2. Find the P-value

The test statistic is

t=(xbar-mu)/(s/vn)

=(6.5-5)/(1.9/sqrt(8))

=2.23

It is a righ-tailed test.

The degree of freedom =n-1=8-1=7

So the p-value= P(t with df=7 >2.23) =0.0305 (from student t table)

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3. Should the pump be put into service? Explain.

Assume that the significant level a=0.05

Since the p-value is less than 0.05, we reject the null hypothesis.

So we can conclude that the pump should be put into service