Suppose it is known from experience that the standard deviation of the weight of all 10-ounce packages of cookies made by a certain bakery is 0.20 ounce. Since the bakery stands to lose money if the average weight of a package of cookies is greater than 10 ounces and since the customer would complain if the average weight of a package of cookies is less than 10 ounces, as part of quality control, the bakery decides to take a simple random sample of 36 packages of cookies and weigh them. The mean weight of the 36 packages of cookies is 10.15 ounces.
a) Test at the 5 % level of significance that the actual mean weight is different from 10 ounces. Write out the hypothesis in words and in symbols; at the end make sure to write out the conclusion for the test.
b) Find and interpret the approximate p-value for the test from part a. Hint: you don't need to use the table or software to find this p-value.
c) What would it mean for bakery's researcher to make a Type I error?