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Kcmayo6019
19.12.2019 •
Mathematics
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 4.6 lbs/square inch. assume the standard deviation is known to be 0.8. if the valve was designed to produce a mean pressure of 4.5 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?
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Ответ:
NO.
Step-by-step explanation:
As per given , we have to test the hypothesis.
∵
is two-tailed , so our test is a two-tailed test.
Also, the standard deviation is known to be 0.8 , so we use z-test.
Test statistic:![z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}](/tpl/images/0425/1613/d79f4.png)
, where
= Sample mean
n= Sample size
Put![\overline{x}=4.6](/tpl/images/0425/1613/879d2.png)
n= 110 , we get
P-value for two tailed test = 2P(Z>|z|)
= 2P(Z>|1.31|) = 2(1-P(Z<1.31)) [∵ P(Z>z)=1-P(Z<z)]
=2(1- 0.9049) [By z-table]
=0.1902
Decision : ∵ P-value (0.1902) > Significance level (0.02).
It means we do not reject the null hypothesis.
[When P-values < Significance level then we reject the null hypothesis.]
Conclusion : We do not have sufficient evidence at the 0.02 level that the valve does not perform to the specifications.
Ответ: