In 2008, Malcolm Gladwell released his book, Outliers. In the book, Gladwell claims that more professional hockey players are born in January through March than in October through December. The following data is a summary of birth months for a random sample of 177 National Hockey League players.

Birth Month Number of Players
January-March 53
April-June 47
July-September 41
October-December 36

Conduct a hypothesis test to determine whether hockey players' birthdays are evenly distributed throughout the year using the stated hypotheses. Let αα = 0.01 and round all numeric results to 4 decimal places.

a. What is the expected value for the number of player birthdays in January - March?
b. Calculate the test statistic for this hypothesis test.
c. Calculate the degrees of freedom for this hypothesis test.
d. Calculate the p-value for this hypothesis test. p-value =
e. What is your conclusion using α = 0.01?