Suppose that a bottled water plant wants to determine if the bacteria count in their water supply exceeds the safety threshold of 100 cfu/mL (colony-forming units per milliliter). Ten different samples were taken at random points in the water supply, and the bacterial count was measured in cfu/mL. The data is presented below: 104 102 100 97 93 105 102 97 96 102

Answer the following four questions on whether the bacteria count in the water supply exceeds the safety threshold of 100 cfu/mL.

Required:
a. Which is appropriate alternative hypothesis?
b. What is the value of t that defines the rejection region for a= 0.01?
c. Using the information in the above two questions, what is the value of the test statistic T?

a

The  alternative hypothesis is  

b

c

d

the decision rule is

      Fail to reject the null hypothesis  

Step-by-step explanation:

From the question we are told that

   The  data given is  

             104 102 100 97 93 105 102 97 96 102

     The  population mean is  

Generally the sample mean is mathematically represented as

=>      

=>    

Generally the standard deviation is mathematically represented as

=>  

=>  

The  null hypothesis is  

The  alternative hypothesis is  

 From the question we are told that the level of significance is  

The  critical value of   is obtained from the normal distribution table  a the value  is  

Generally the test statistic is mathematically represented as

=>      

=>      

From the value  obtained and the value calculated we see that the critical value is not within the region of  rejection(i.e -1.7186 to +  -1.7186 ) hence we fail to  reject the null hypothesis

Thus  the decision rule is

      Fail to reject the null hypothesis