A researcher claims that the number of violent crimes in England and Wales by year is uniformly distributed. To test this claim, you randomly select 22,526 crimes from recent years and record the year when each happened. The table shows the results. At \(\alpha=0.05\), test the researcher's claim.

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) find the critical value and identify the rejection region,

(c) find the chi-square test statistic,

(d) decide whether to reject or fail to reject the null hypothesis, and

(e) interpret the decision in the context of the original claim.

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Year Frequency, f Year Frequency, f 2003 2307 2009 1774 2004 2213 2010 1687 2005 2010 2011 1896 2006 1984 2012 1744 2007 2103 2013 1666 2008 1815 2014 1327