An engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 150 engines and the mean pressure was 7.7 lbs/square inch. assume the standard deviation is known to be 0.5. if the valve was designed to produce a mean pressure of 7.6 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications? state the null and alternative hypotheses for the above scenario.

We are given that The valve was tested on 150 engines and the mean pressure was 7.7 lbs/square inch.

We are also given that the valve was designed to produce a mean pressure of 7.6 lbs/square inch

So,

Null hypothesis:

Alternate hypothesis :  

Since n > 30 and population standard deviation is given

So, We will use z test

Formula :

Substitute the values

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

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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step-by-step explanation: