A large farm selling round fescue hay bales claims the mean weight per bale is 1600 pounds. To check this claim, personnel from the local agricultural extension service randomly selected 25 round...

A large farm selling round fescue hay bales claims the mean weight per bale is 1600 pounds. To check this claim, personnel from the local agricultural extension service randomly selected 25 round bales and carefully weighed each. The sample mean was
 pounds. Assume the underlying population is normal and

a. Is there any evidence to suggest that the true mean weight of these round hay bales is less than 1600 pounds? Use
 and compute the p value to draw a conclusion.

b. Carefully sketch a graph to illustrate the p value in this hypothesis test.

A technical panel investigating residential smoke alarms recommends that the sound emitted by the device (during a fire) should be at least 85 decibels at 10 feet away. In a random sample of 60 smoke alarms from homes in a large city, the sample mean decibel level (at 10 feet away) was
  Assume

a. Is there any evidence that the true mean decibel level produced by smoke alarms in this city is less than 85? Use
 and compute the p value to draw a conclusion.

 b. What is the smallest significance level at which this hypothesis test would be significant?