The U. S. Department of Agriculture claims that the mean consumption of coffee by a person in the United States is 24.2 gallons per year. A random sample of 101 people in the United States shows that the mean coffee consumption is 23.5 gallons per year with a standard deviation of 3.2 gallons. At α=0.05, can you reject the claim? Using a P-value, evaluate the claim. Using Rejection Regions for a z-test, evaluate the claim.

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim  

Step-by-step explanation:

From the question we are told that

   The population mean is  

    The sample size is  n  =  101

     The sample mean is  

     The standard deviation is  

The null hypothesis is  

 The alternative hypothesis is

Generally the test statistics is mathematically represented as    

=>              

=>            

From the z table  the area under the normal curve to the left corresponding to    -2.198  is  

Gnerally the  p-value is mathematically represented as

=>      

From the value obtained we have that   hence  

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim  

Using the Rejection Regions for a z-test method

Generally from the z table  the critical value  of  is  

Not we are using    because it is a two - tailed test

   Now comparing the critical value and the test statistics we see that the

region covered by  the test statistics (i.e )   is greater than the region covered by  the critical value  (i.e )

Hence

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim