An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 250 engines and the mean pressure was 7.8 lbs/square inch. Assume the 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.
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 7.9 lbs/square inch.
Alternative hypothesis: Ha: The mean pressure of the value is less than 7.9 lbs/square inch.
H0: µ = 7.9 versus Ha: µ < 7.9
This is a lower tailed or left tailed test.
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