12.10 The report referenced in the previous exercise

(“Fatality Facts 2004: Bicycles”) also classified 719 fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table.

Month Number of Accidents January 38 February 32 March 43 April 59 May 78 June 74 July 98 August 85 September 64 October 66 November 42 December 40

a. Use the given data to test the null hypothesis H0: p1 5 1/12, p2  1/12, ... , p12  1/12, where p1 is the proportion of fatal bicycle accidents that occur in January, p2 is the proportion for February, and so on. Use a significance level of .01.

b. The null hypothesis in Part

(a) specifies that fatal accidents were equally likely to occur in any of the 12 months. But not all months have the same number of days. What null and alternative hypotheses would you test to determine if some months are riskier than others if you wanted to take differing month lengths into account? (Hint: 2004 was a leap year, with 366 days.)

c. Test the hypotheses proposed in Part

(b) using a .05 significance level.