An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.6 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 160 engines and the mean pressure was 5.7 pounds/square inch. Assume the variance is known to be 0.25. A level of significance of 0.01 will be used. Make a decision to reject or fail to reject the null hypothesis.

The decision rule is  

Reject the null hypothesis  

Step-by-step explanation:

From the question we are told that

    The population mean is

     The  sample size is  n =  160

      The sample mean is  

     The variance is

       The level of significance is  

The null hypothesis is  

The alternative hypothesis is

Generally the standard deviation is mathematically represented as

=>          

=>          

Generally the test statistics is mathematically represented as

=>      

=>    

From the z table  the area under the normal curve to the left corresponding to  2.53   is

From the value obtained we see that the hence

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to conclude that the believe  that the valve performs above the specifications is true

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!