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\fLife after death and gender In the 2012 GSS, 605 of 790 males and 822 of 977 females indicated a belief in life after death. (Source: Data from CSM. UC Berkeley.) a. Construct a 2 x 2 contingency table relating gender of respondent (SEX, categories male and female) as the rows to belief about life after death (POSTLIFE, categories yes and no) as the columns. b. Find the four expected cell counts when assuming independence. Compare them to the observed cell counts, identifying cells having more observations than expected. c. For this data, X" = 18.0. Verify this value by plugging into the formula for X" and computing the Sum.Happiness and gender For the 2 x 3 table on gender and happiness in Exercise 11.4 (shown below), software tells us that X" = 1.04 and the P-value = 0.59. Happiness Gender Not Pretty Very Female 154 592 336 Male 123 502 257 3. State the null and alternative hypothesis, in context, to which these results apply. b. Interpret the P-value. Reference: Exercise 11.4 11.14 Smoking and alcohol Refer to the previous exercise. A similar table relates cigarette use to alcohol use. The MINITAB output for the chi-squared test follows. a. True or false: If we use cigarette use as the column variable and alcohol use as the row variable, then we will get different values for the chi-squared statistic and the P-value shown in the output. b. Explain what value you would get for the z statistic and P-value if you conducted a significance test of Ho: pi = p2 against He: p, # pz, where pi is the pop- ulation proportion of non-cigarette users who have drunk alcohol and pz is the population proportion of cigarette users who have drunk alcohol. Dayton student survey Row: cigarette Columns: alcohol no yes no 281 500 yes 46 1449 Pearson Chi-Square - 451 . 404, DF = 1, P-value = 0. 000What gives P-value = 0.05? How large a X2 test statistic value provides a P-value of 0.05 for testing independence for the following table dimensions? a. 2x 2 b. 2x3 C. 2 x 5 d. 5x5 e. 3x9Marital happiness and income In Exercise 11.5 when you used the GSS to download a 3 x 3 table for family income and marital happiness in 2012, you should have obtained results similar to the following table. Marital Happiness Income Not Pretty Very Above 62 139 Average 125 283 Below 6 69 115 a. State the null and alternative hypotheses for the test. b. What is the number of degrees of freedom for the chi-squared test? C. The chi-squared statistic for the table equals X" = 4.58. (@) What value do you expect for X if the null hypothesis were true? (ii) How many standard deviations is 4.58 from this expected V2 x df). (mi) Is X
