Part of the assembly line will need adjusting if the consistency of the injected plastic becomes either too viscous or not viscous enough as compared with a value (56.00) your engineers consider reasonable. You will decide to adjust only if you are convinced that the system is “not in control,” that is, there is a real need for adjustment. The average viscosity for 13 recent measurements was 51.22 with a standard error of 3.18. 

a. Identify the null and research hypotheses for a two-sided test, using both words and mathematical symbols. 

b. Perform a two-sided test at the 5% significance level and describe the result. 

c. Perform a two-sided test at the 1% significance level and describe the result. 

d. State the p-value as either p>0.05, p<0.05, p<0.01, or p<0.001. 

e. Find the p-value using statistical software