A machine is designed to fill automobile tires to a mean air pressure of 30 pounds per square inch (psi). The manufacturer tests the machine on a random sample of 12 tires. The air pressures for these tires are shown below:
30.4 31.1 29.8 30.3 31.7 28.9 32.4 30.3 29.7 31.6 30.8 30.2

Fill pressures for the machine are known to follow a normal distribution with standard deviation 1.2 psi.

(a) Construct a 90% confidence interval for the true mean fill pressure for this machine. Round your answers to two decimal places.

(b) Provide an interpretation of the confidence interval in (a).

(c) Use JMP to conduct a hypothesis test at the 10% level of significance to determine whether the true mean fill pressure for the machine differs from 30 psi. Upload the ouput in your answer. JMP will give you the value of the test statistic and the P-value, but you will need to prepare out the hypotheses and conclusion.

(d) Provide an interpretation of the P-value of the test in (c).

(e) Could you have used the confidence interval in (a) to conduct the test in (c)? If no, describe why not. If yes, describe why, and describe what your conclusion would have been and why.