A report classified fatal bicycle accidents according to themonth in which the accident occurred, resulting in the accompanyingtable.
| Month | Number of Accidents |
|---|
| January | 40 |
| February | 30 |
| March | 45 |
| April | 59 |
| May | 76 |
| June | 72 |
| July | 100 |
| August | 87 |
| September | 66 |
| October | 64 |
| November | 40 |
| December | 38 |
(a) Use the given data to test the null hypothesisH0: p1 =1/12, p2= 1/12, .., p12=1/12, where p1 is the proportion of fatal bicycle accidents thatoccur in January, p2 is the proportion for February, and so on. Usea significance level of 0.01.
Calculate the test statistic. (Round your answer to two decimalplaces.)
?2 =
What is the P-value for the test? (Use a statisticalcomputer package to calculate the P-value. Round youranswer to four decimal places.)
P-value =
What can you conclude?
Reject H0. There is not enough evidence toconclude that fatal bicycle accidents are not equally likely tooccur in each of the months.
Do not reject H0. There is not enough evidenceto conclude that fatal bicycle accidents are not equally likely tooccur in each of the months.
Do not reject H0. There is convincing evidenceto conclude that fatal bicycle accidents are not equally likely tooccur in each of the months.
Reject H0. There is convincing evidence toconclude that fatal bicycle accidents are not equally likely tooccur in each of the months.
(b) The null hypothesis in part (a) specifies that fatalaccidents were equally likely to occur in any of the 12 months. Butnot all months have the same number of days. What null andalternative hypotheses would you test to determine if some monthsare riskier than others if you wanted to take differing monthlengths into account? (Assume this data was collected during a leapyear, with 366 days.) (Enter your probabilities as fractions.)
Identify the null hypothesis by specifying the proportions ofaccidents we expect to occur in each month if the length of themonth is taken into account. (Enter your probabilities asfractions.)
p1= p2=p3= p4=p5= p6= p7= p8=p9= p10=p11= p12=
Identify the correct alternative hypothesis.
H0 is true. None of the proportions is notcorrectly specified under H0.
H0 is not true. At least one of the proportionsis not correctly specified under H0.
H0 is true. At least one of the proportions isnot correctly specified under H0.
H0 is not true. None of the proportions iscorrectly specified under H0.
(c) Test the hypotheses proposed in part (b) using a 0.05significance level.
Calculate the test statistic. (Round your answer to two decimalplaces.)
?2 =
What is the P-value for the test? (Use a statisticalcomputer package to calculate the P-value. Round youranswer to four decimal places.)
P-value =
What can you conclude?
Reject H0. There is not enough evidence toconclude that fatal bicycle accidents do not occur in the twelvemonths in proportion to the lengths of the months.
Do not reject H0. There is convincing evidenceto conclude that fatal bicycle accidents do not occur in the twelvemonths in proportion to the lengths of the months.
Do not reject H0. There is not enough evidenceto conclude that fatal bicycle accidents do not occur in the twelvemonths in proportion to the lengths of the months.
Reject H0. There is convincing evidence toconclude that fatal bicycle accidents do not occur in the twelvemonths in proportion to the lengths of the months.
