Q1 [13 pts] Chi-square test about 2-way table A 2017 Gallup poll asked a sample of...

 

 

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Q1 [13 pts] Chi-square test about 2-way table A 2017 Gallup poll asked a sample of smokers several questions about their smoking habits and beliefs about smoking. Two of the questions asked on the survey were "In general, how harmful do you feel second-hand smoke is to adults - very harmful, somewhat harmful, not too harmful or not at all harmful?" and "How many packs of cigarettes do you smoke per day", here is a two-way table of the results: Cigarettes Per day Less than One pack More than Row Sum one pack one pack Very harmful 797 228 63 1088 Somewhat harmful 777 446 120 1343 Not too harmful 263 179 69 511 Not at all harmful 155 139 63 357 Column sum 1992 992 315 3299 (a) [1 pt] What is the percentage of smokers in the sample who feel second-hand smoke is very harmful? (b) [2 pts] What is the percentage of smokers who smoke more than one pack of cigarettes per day who feel second-hand smoke is very harmful? (c) [3 pts] Find three missing counts (A), (B) and (C), in the following expected counts table. Show details of your calculation. Cigarettes Per day Less than One pack More than one pack one pack Very harmful (A) 327.159 (B) Somewhat harmful 810.929 403.836 128.224 Not too harmful 308.552 153.656 48.792 Not at all harmful 214.564 107.349 (C) (d) [2 pts] For this two-way table, which type is the chi-square test in this case? Homogeneity, independent or goodness of fit? And what is the degrees of freedom for this chi-square test? (e) [2 pts] Calculate the contribution of this cell of smokers who smoke more than one pack of cigarettes per day and smokers who feel second-hand smoke is somewhat harmful? i.e. find (observed - expected)/expected, round your result up to 3 decimal places. (f) [3 pts] Using an appropriate Shiny App to find the chi-square test, what is the chi-square test statistic value and p-value, respectively? What conclusion do you have at 5% significance level? Q1 [13 pts] Chi-square test about 2-way table A 2017 Gallup poll asked a sample of smokers several questions about their smoking habits and beliefs about smoking. Two of the questions asked on the survey were "In general, how harmful do you feel second-hand smoke is to adults - very harmful, somewhat harmful, not too harmful or not at all harmful?" and "How many packs of cigarettes do you smoke per day", here is a two-way table of the results: Cigarettes Per day Less than One pack More than Row Sum one pack one pack Very harmful 797 228 63 1088 Somewhat harmful 777 446 120 1343 Not too harmful 263 179 69 511 Not at all harmful 155 139 63 357 Column sum 1992 992 315 3299 (a) [1 pt] What is the percentage of smokers in the sample who feel second-hand smoke is very harmful? (b) [2 pts] What is the percentage of smokers who smoke more than one pack of cigarettes per day who feel second-hand smoke is very harmful? (c) [3 pts] Find three missing counts (A), (B) and (C), in the following expected counts table. Show details of your calculation. Cigarettes Per day Less than One pack More than one pack one pack Very harmful (A) 327.159 (B) Somewhat harmful 810.929 403.836 128.224 Not too harmful 308.552 153.656 48.792 Not at all harmful 214.564 107.349 (C) (d) [2 pts] For this two-way table, which type is the chi-square test in this case? Homogeneity, independent or goodness of fit? And what is the degrees of freedom for this chi-square test? (e) [2 pts] Calculate the contribution of this cell of smokers who smoke more than one pack of cigarettes per day and smokers who feel second-hand smoke is somewhat harmful? i.e. find (observed - expected)/expected, round your result up to 3 decimal places. (f) [3 pts] Using an appropriate Shiny App to find the chi-square test, what is the chi-square test statistic value and p-value, respectively? What conclusion do you have at 5% significance level?