A report classified fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table.MonthNumber of AccidentsJanuary36February34March45April57May78June72July98August85September66October64November40December40(a)Use the given data to test the null hypothesisH0: p1 = 112, p2 = 112, , p12 = 112,wherep1is the proportion of fatal bicycle accidents that occur in January,p2is the proportion for February, and so on. Use a significance level of 0.01.Calculate the test statistic. (Round your answer to two decimal places.)χ2 =What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.)P-value =What can you conclude?Do not reject H0. There is not enough evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.Do not reject H0. There is convincing evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months. Reject H0. There is not enough evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months. Reject H0. There is convincing evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.(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? (Assume this data was collected during a leap year, with 366 days.) (Enter your probabilities as fractions.)Identify the null hypothesis by specifying the proportions of accidents we expect to occur in each month if the length of the month is taken into account. (Enter your probabilities as fractions.)p1= p2= p3= p4= p5= p6= p7= p8= p9= p10= p11= p12=Identify the correct alternative hypothesis.H0 is not true. None of the proportions is correctly specified under H0.H0 is true. At least one of the proportions is not correctly specified under H0. H0 is true. None of the proportions is not correctly specified under H0. H0 is not true. At least one of the proportions is not correctly specified under H0.(c)Test the hypotheses proposed in part (b) using a 0.05 significance level.Calculate the test statistic. (Round your answer to two decimal places.)χ2 =What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.)P-value =What can you conclude?Reject H0. There is not enough evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months. Reject H0. There is convincing evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months. Do not reject H0. There is not enough evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.Do not reject H0. There is convincing evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.

Question

A report classified fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table.MonthNumber of AccidentsJanuary36February34March45April57May78June72July98August85September66October64November40December40(a)Use the given data to test the null hypothesisH0: p1 = 112, p2 = 112,    , p12 = 112,wherep1is the proportion of fatal bicycle accidents that occur in January,p2is the proportion for February, and so on. Use a significance level of 0.01.Calculate the test statistic. (Round your answer to two decimal places.)χ2 =What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.)P-value =What can you conclude?Do not reject H0. There is not enough evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.Do not reject H0. There is convincing evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.      Reject H0. There is not enough evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months. Reject H0. There is convincing evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.(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? (Assume this data was collected during a leap year, with 366 days.) (Enter your probabilities as fractions.)Identify the null hypothesis by specifying the proportions of accidents we expect to occur in each month if the length of the month is taken into account. (Enter your probabilities as fractions.)p1= p2= p3= p4= p5= p6= p7= p8= p9= p10= p11= p12=Identify the correct alternative hypothesis.H0 is not true. None of the proportions is correctly specified under H0.H0 is true. At least one of the proportions is not correctly specified under H0.     H0 is true. None of the proportions is not correctly specified under H0. H0 is not true. At least one of the proportions is not correctly specified under H0.(c)Test the hypotheses proposed in part (b) using a 0.05 significance level.Calculate the test statistic. (Round your answer to two decimal places.)χ2 =What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.)P-value =What can you conclude?Reject H0. There is not enough evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months. Reject H0. There is convincing evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.      Do not reject H0. There is not enough evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.Do not reject H0. There is convincing evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.

Accepted Answer

a) 
Null hypothesis: P1=P2 Alternative hypothesis: P1 ≠P2
Note that these hypotheses constitute a…

Month	Number of Accidents
January	36
February	34
March	45
April	57
May	78
June	72
July	98
August	85
September	66
October	64
November	40
December	40

A report classified fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table. Month Number of Accidents January 36 February 34 March 45 April 57 May 78 June 72 July 98 August 85 September 66 October 64 November 40 December 40