An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines and the mean pressure was 7.1 lbs/square inch. Assume the variance is known to be 0.64. If the valve was designed to produce a mean pressure of 7 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.
H0 =
Ha =
Solution :
Given that,
Population mean = = 7
Sample mean = = 7.1
Sample standard deviation = s = 0.8
Sample size = n = 110
Level of significance = = 0.01
This is a two tailed test.
The null and alternative hypothesis is,
Ho: 7
Ha: 7
The test statistics,
t = ( - )/ (s/)
= ( 7.1 - 7 ) / ( 0.8 / 110 )
= 1.311
Critical value of the significance level is α = 0.01, and the critical value for a two-tailed test is
= 2.622
Since it is observed that |t| =1.311 = 2.622 , it is then concluded that the null hypothesis is fail to rejected.
P- Value = 0.1926
The p-value is p = 0.1926 > 0.01, it is concluded that the null hypothesis is fail to rejected.
Conclusion :
It is concluded that the null hypothesis Ho is fail to rejected. Therefore, there is not enough evidence to claim that the valve was designed to produce a mean pressure of 7 lbs/square inch, at the 0.01 significance level.
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