For all problems, round every calculation to three decimal places. Show work

1. In order to determine how long geese need to be in a place before they start nesting, Rahma has been carefully watching a particular section of the Arctic for the arrival of various geese and when they first start nesting. She is concerned that if the average time between arrival and nesting is greater than 16 days, that they may eventually not nest before returning south. She studied 54 geese and found that that the mean time between arrival and nesting was 17.9 days with a standard deviation of 5.1 days.
   1. What are the null and alternative hypotheses for this test?
   2. Check to be sure you may use Normal distribution calculations for this hypothesis test. (Apply the CLT)
   3. Calculate the standard error.
   4. Calculate the test statistic.
   5. Find the p-value. Indicate how you get this value in StatKey. In particular, mention what value you used for your degrees of freedom.
   6. What is the conclusion of the test in context of the problem?