Answer:
a
 The null hypothesis is  
The alternative hypothesis is  
 The null hypothesis is rejected
b
The  99% confidence level is   
Step-by-step explanation:
From the question we are told that 
   The sample size is  n =  10
    The  population mean is  
    The level of significance is  
    The  sample data is  
13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002
Generally the sample mean is mathematically represented as 
         
=>     
Generally the sample standard deviation  is mathematically represented as
     
=> 
=>  
The null hypothesis is  
The alternative hypothesis is  
Generally the test statistics is mathematically represented as 
       
=>    
=>   
Generally the p-value is mathematically represented as 
        
From the z-table  
So 
        
       
So from the obtained value we see that 
      
Hence the null hypothesis is rejected 
Consider the b question 
Given that the confidence level is  99%  then the level of significance is 
     
=>  
 
Generally from the normal distribution table critical value  of   is
 is  
     
Generally the margin of error is mathematically represented as  
      
=>   
=>    
Generally the 99% confidence interval is mathematically represented as 
      
=>   