You wish to test the following claim ($\displaystyle {H}_{{a}}$) at a significance level of $\displaystyle \alpha={0.002}$.      

$\displaystyle {H}_{{o}}:\mu={53.7}$
$\displaystyle {H}_{{a}}:\mu\ne{53.7}$

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size $\displaystyle {n}={19}$ with mean $\displaystyle \overline{{x}}={51.1}$ and a standard deviation of $\displaystyle {s}={15.9}$.

1. What is the test statistic for this sample?
   
   test statistic = Round to 3 decimal places
   
   
2. What is the p-value for this sample?
   
   p-value = Use Technology Round to 4 decimal places.
   
   
3. The p-value is...
   • less than (or equal to) $\displaystyle \alpha$
   • greater than $\displaystyle \alpha$
   
   
   
4. This test statistic leads to a decision to...
   
   • reject the null
   • accept the null
   • fail to reject the null
   
   
   
5. As such, the final conclusion is that...
   
   • There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 53.7.
   • There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 53.7.
   • The sample data support the claim that the population mean is not equal to 53.7.
   • There is not sufficient sample evidence to support the claim that the population mean is not equal to 53.7.