Answer:
We are given that The valve was tested on 150 engines and the mean pressure was 7.7 lbs/square inch.
[tex]\bar{x}=7.7\\n = 150 \\\sigma = 0.5[/tex]
We are also given that the valve was designed to produce a mean pressure of 7.6 lbs/square inch
So, [tex]\mu = 7.6[/tex]
Null hypothesis: [tex]H_0:\mu = 7.6[/tex]
Alternate hypothesis : [tex]H_a:\mu \neq 7.6[/tex]
Since n > 30 and population standard deviation is given
So, We will use z test
Formula : [tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Substitute the values
[tex]z=\frac{7.7-7.6}{\frac{0.5}{\sqrt{150}}}[/tex]
[tex]z=2.449[/tex]
refer the z table for p value
so, p value is 0.9927
Since it is a two tailed test So, p = 2(1- 0.9927) = 0.0146
α = 0.1
p value< α
So, we reject null hypothesis
Hence There is sufficient evidence at the 0.1 level that the valve does not perform to the specifications
The null hypothesis is that the mean is equal to 7.6 lbs while the alternate hypothesis of the valve is that it is not equal to 7.6lbs.
This term is used to refer to a statement which is made that is tested to be true or untrue during the study.
The Null hypothesis
H0: μ = 7.6
The alternate hypothesis:
H1: μ ≠ 7.6
The null hypothesis says the valve produces a mean pressure of 7.6 lbs. The alternate hypothesis on the other hand says that it does not.
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