A particular report classified 717 fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table.
Month Number of Accidents
January 37
February 32
March 42
April 59
May 78
June 74
July 97
August 83
September 64
October 67
November 44
December 40
(a) Use the given data to test the null hypothesis H0: p1 = 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. (Round your χ2 value to two decimal places, and round your P-value to three decimal places.)
χ2 =
P-value =
What can you conclude?
(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?
H0: p1 = 31/365, p2 = 28/365, ..., p12 = 31/365
Ha: At least one of the true category proportions differs from the hypothesized value.
H0: p1 = 31/365, p2 = 28/365, ..., p12 = 31/365
Ha: All of the true category proportions differ from the hypothesized values.
H0: p1 = 30/365, p2 = 30/365, ..., p12 = 30/365
Ha: At least one of the true category proportions differs from the hypothesized value.
H0: p1 = 30/365, p2 = 30/365, ..., p12 = 30/365
Ha: All of the true category proportions differ from the hypothesized values.
(c) Test the hypothesis proposed in Part (b) using a .05 significance level. (Round your χ2 value to two decimal places, and round your P-value to three decimal places.)
χ2 =
P-value =
What can you conclude?