Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 5.8 lbs/square inch. Assume the standard deviation is known to be 0.64. If the valve was designed to produce a mean pressure of 5.6 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve performs above the specifications?

State the null and alternative hypotheses for the above scenario.

Answer #1

Solution:

For the given scenario, we need to use the one sample z test for the population mean, because we are given the value for the population standard deviation. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: The mean pressure of the valve is 5.6 lbs/square inch.

Alternative hypothesis: Ha: The mean pressure of the value is greater than 5.6 lbs/square inch.

H0: µ = 5.6 versus Ha: µ > 5.6

This is an upper tailed or right tailed test.

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standard deviation is known to be 0.8. If the valve was designed to
produce a mean pressure of 7.9 lbs/square inch, is there sufficient
evidence at the 0.05 level that the valve performs below the
specifications?
State the null and alternative hypotheses for the above
scenario.

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pressure on an automobile engine. The valve was tested on 170
engines and the mean pressure was 6.5 lbs/square inch. Assume the
standard deviation is known to be 1. If the valve was designed to
produce a mean pressure of 6.6 lbs/square inch, is there sufficient
evidence at the 0.05 level that the valve performs below the
specifications? State the null and alternative hypotheses for the
above scenario.

An engineer has designed a valve that will regulate water
pressure on an automobile engine. The valve was tested on 280
engines and the mean pressure was 6.6 lbs/square inch. Assume the
variance is known to be 1. If the valve was designed to produce a
mean pressure of 6.7 lbs/square inch, is there sufficient evidence
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specifications?
State the null and alternative hypotheses for the above
scenario.

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engines and the mean pressure was 6.6 lbs/square inch. Assume the
standard deviation is known to be 1. If the valve was designed to
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