Suppose a production line operates with a mean filling weight of 16 ounces per container. Since over- or under-filling can be dangerous, a quality control inspector samples 30 items to determine whether or not the filling weight has to be adjusted. The sample revealed a mean of 16.32 ounces. From past data, the population standard deviation is known to be 0.8 ounces. Using a 0.10 level of significance, can it be concluded that the process is out of control (not equal to 16 ounces). Step 1: State hypotheses:
Step 2: State the test statistic. Since we know the population standard deviation and the sample is large our test statistics is
Step 3: State the critical region(s):
Step 4: Conduct the experiment/study:
Step 5: Reach conclusions and state in English:
Step 6: Calculate the p-value associated with this test. How does this the p-value support your conclusions in Step 5?

From the question we are told that

   The  population mean is  

    The sample size is  n  =  30  

     The  sample mean is  

     The  population standard deviation is  

      The  level of significance is  

Step 1: State hypotheses:

The  null hypothesis is  

The alternative hypothesis is  

Step 2: State the test statistic. Since we know the population standard deviation and the sample is large our test statistics is

=>      

=>      

Generally the degree of freedom is mathematically represented as

=>      

=>      

Step 3: State the critical region(s):

From the student t-distribution table the critical value corresponding to    is

Generally the critical regions is mathematically represented as  

Step 4: Conduct the experiment/study:

Generally the from the value obtained we see that the t value is outside the critical region so  the decision is [Reject the null hypothesis ]  

Step 5: Reach conclusions and state in English:

  There is  sufficient evidence to show that the filling weight has to be adjusted

Step 6: Calculate the p-value associated with this test. How does this the p-value support your conclusions in Step 5?

From the student t-distribution table the probability value to the right corresponding to at  a degree of freedom of    is

Generally the p-value is mathematically represented as

=>    

=>    

Generally  looking at the value obtained we see that hence

The decision rule is

Reject the null hypothesis

Step-by-step explanation:

b

step-by-step explanation:

$18 was the price of the t-shirt

step-by-step explanation: