200 males and 200 females are asked a series of questions to determine whether they are considered heavy drinkers or not. 66 of the males are considered heavy drinkers. 83 of the females are classified as heavy drinkers. Execute a hypothesis test as to whether there is a relationship between gender and drinking at alpha=0.05 USING CHI-SQUARE. State Ho and Ha, calculate the p-value, determine whether you reject Ho and state the conclusion in plain English.

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vzletanje8z0 · Accepted Answer

Given information:200 males and 200 females are asked whether they are heavy drinkers or not.66 males out of 200 are considered as heavy drinkers.83 out of 200 females are considered to be heavy drinkers.The null and alternate hypothesis for testing is defined as,Ho : There is no relationship between gender and drinking.Ha : There is a significant relationship between gender and drinking.The test is performed at 0.05 level of significance using Chi-square test of independence.The observed values are, (Table 1) GENDER  Heavy Drinkers  Not Heavy Drinkers  Total  Female 83200−83=117200 Male 66200−66=134200 Total 149251400The expected values are calculated as, GENDER  Heavy Drinkers  Not Heavy Drinkers  Total  Female =200×149400=200×251400200 Male =200×149400200×251400200 Total 149251400Thus, the expected values are, (Table 2) GENDER  Heavy Drinkers  Not Heavy Drinkers  Total  Female 74.5125.5200 Male 74.5125.5200 Total 149251400The chi-square test statistics is computed as,χ2=∑i(Oi−Ei)2Eiwhere, Oi are the observed frequencies tabulated in Table 1.and, Ei are the expected frequencies as calculated in Table 2.Thus, the chi-square test statistics is,χ2=(83−74.5)274.5+(117−125.2)2125.5+(66−74.5)274.5+(134−125.5)2125.5=3.091The chi-square test statistics is 3.091 .The degree of freedom (dof) for the test is computed as,dof=(number of rows−1)(number of colums−1)=(2−1)(2−1)=1The p-value for the calculated value of chi-square test statistics is computed as,p−value=P(χ2&amp;gt;χ2)=P(χ2&amp;gt;3.091)=0.0787 Thus, the p-value for the chi-square test is 0.0787 which is greater than the level of significance (0.05) of the test; so, the decision is fail to reject Ho.In conclusion, there is no sufficient evidence to support that there is a relationship between the gender and the drinking.

200 males and 200 females are asked a series of questions to determine whether they are considered h

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