For the following problem, provide the following:Test statisticp-valueInterpretation of the results in the context of the problemCases of UFO sightings are randomly selected and categorized according to month, with the results listed in the table below (based on data from Larry Hatch). Use a .05 significance level to test the claim that UFO sightings occur in the different months with equal frequency. Is there any reasonable explanation for the two months that have the highest frequencies? Month: 1 2 3 4 5 6 7 8 9 10 11 12 1239 1111 1428 1276 1102 1225 2233 2012 1680 1994 1648 1125

Null hypothesis: H0: The UFO sightings occur in the different months with equal frequency. Alternate hypothesis: HA: The UFO sightings occur in the different months with unequal frequency. For this analysis, the significance level is 0.05. Using the sample data, we will a chi-square goodness of fit test of the null hypothesis. Use the given data to form excel table consisting of observed frequency, expected probability, expected frequency and chi square statistics. Observed frequency P(x) Expected frequency (Or,c-Er,c)2Er,c January 1239 0.0833 1506.0833 47.3635856434081 February 1111 0.0833 1506.0833 103.64024142828 March 1428 0.0833 1506.0833 4.04825337981117 April 1276 0.0833 1506.0833 35.1496753905448 May 1102 0.0833 1506.0833 108.415873586748 June 1225 0.0833 1506.0833 52.459142551503 July 2233 0.0833 1506.0833 350.84900588355 August 2012 0.0833 1506.0833 169.945226765528 September 1680 0.0833 1506.0833 20.0832226710202 October 1994 0.0833 1506.0833 158.067397960127 November 1648 0.0833 1506.0833 13.3726599531536 December 1125 0.0833 1506.0833 96.4252798834342 Sum 18073 1 18073 1159.81956509711 Formula for the expected frequency is: E(x)=n×pi DF = k - 1 D.F = 12 - 1 D.F = 11 Use the table to determine the chi-square statistic, degree of freedom and P-value. χ 2=∑(Or,c-Er,c)2Er,c =1159.81956509711=1159.82Use the excel formula, "=CHISQ.DIST.RT(1159.82,11)" for determining the P-value from the chi-square statistic having degrees of freedom 11. P(χ2>1159.82)=0.000 Since the P-value (0.000) is less than the significance level (0.05), we have to reject the null hypothesis. We have to Reject H0. There is convincing evidence to conclude that UFO sightings occur in the different months with unequal frequency. Two months that have the highest frequencies are July and August, because these months have rainy season and hence Cases of UFO sightings is more usual in these months.