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

A)State the appropriate null and alternate hypotheses.

H₀ : ? ? 5 versus H₁ : ? ? 5

H₀ : ? = 5 versus H₁ : ? ? 5

H₀ : ? ? 5 versus H₁ : ? > 5

B)What is the P-value?

0.1 < P < 0.25

0.025 < P < 0.05

0.001 < P < 0.005

0.25 < P < 0.4

P < 0.0005

0.01 < P < 0.025

0.0005 < P < 0.001

P > 0.4

0.005 < P < 0.01

0.05 < P < 0.1

C)Should the pump be put into service? Explain.

No, the P-value is small, so we conclude that ? ? 5.

Yes, the P-value is large, so we conclude that ? > 5.

No, the P-value is large, so we conclude that ? ? 5.

Yes, the P-value is small, so we conclude that ? > 5.

Answer 1

Solution: Sample size n 8 Sample mean 6.5 Sample standard deviation S 1.9 Part-A: Null Hypothesis: Alternate Hypothesis: Ha: u>5 Part-B: Degrees of Freedom: df-n -1 8 17 Test Statistic: 6.5 5 1.9/V8 t 2.233 From t-distribution table; area under the curve to the right of (t 2.233) and for (df-7) is given by 0.0304 Hence, P-value = 0.0304

Part-C: Yes, the pump should be put into service. The P-value is small, so we conclude that μ > 5.