Pizza delivery place claims that they can have a pie in your hand in no more than 30 minutes. A random sample of 14 deliveries gave a mean delivery time of 30 minutes and 40 seconds with a standard deviation s of 5 minutes and 51 seconds. Assume that the delivery times are normally distributed. Based on the sample, is the delivery time is greater than the advertised 30 minutes? Use 0.05 as the level of significance.

 For each of the following problems, please provide the requested information.

(a) What is the level of significance? State the null and alternative hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? 


(b) Identify the sampling distribution you will use: the standard normal or Student's t. Explain the rationale for your choice. What is the value of the sample test statistic? 


(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value. 


(d) Find the critical value(s).