Identify each of the following statements as true or false:
", "advice": "Revise $\\chi^2$ testing, e.g., Sections 6.3 and 6.4 of OpenIntro Statistics (4th edition).
\nTo obtain a p-value from a $\\chi^2$ statistic, use relevant software (e.g., the Excel function CHI.DIST.RT).
", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"t_statements": {"name": "t_statements", "group": "Statements", "definition": "[ \"The chi-square distribution is defined by one parameter: the number of degrees of freedom.\", \"The chi-square statistic is always positive.\", \"The chi-square test should not be used if an expected outcome is less than 5. \", \"As the degrees of freedom increases, the shape of the chi-square distribution becomes more symmetric.\", \"For a one-way table with $\\\\var{groupsTrue}$ groups, $df = \\\\var{dfTrue}$.\", \"If $\\\\chi^2 = \\\\var{Chi2small}$ with $df = 5$, you cannot reject H0 at the $5\\\\%$ significance level.\", \"If $\\\\chi^2 = \\\\var{Chi2large}$ with $df = 5$, you reject H$_0$ at the $5\\\\%$ significance level.\", \"When finding the p-value of a chi-square test, we consider the area in the right tail only.\", \"For a $\\\\var{nRows}\\\\times\\\\var{nCols}$ two-way table, $df=\\\\var{df}$.\", \"A one-way table describes counts for each outcome in a single variable.\", \"A two-way table describes counts for combinations of outcomes for two variables.\", \"The chi-square test is appropriate for categorical data.\" ]", "description": "", "templateType": "list of strings", "can_override": false}, "nRows": {"name": "nRows", "group": "Statements", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "Chi2large": {"name": "Chi2large", "group": "Statements", "definition": "random(12..20#0.1)", "description": "", "templateType": "anything", "can_override": false}, "statements": {"name": "statements", "group": "Statements", "definition": "t_statements+f_statements", "description": "", "templateType": "anything", "can_override": false}, "Chi2small": {"name": "Chi2small", "group": "Statements", "definition": "random(1..9#0.1)", "description": "", "templateType": "anything", "can_override": false}, "nCols": {"name": "nCols", "group": "Statements", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "f_statements": {"name": "f_statements", "group": "Statements", "definition": "[ \"The chi-square distribution is defined by two parameters: mean and standard deviation.\", \"The chi-square statistic can be positive or negative.\", \"The chi-square test should not be used if an expected outcome is greater than 5. \", \"As the degrees of freedom increases, the shape of the chi-square distribution becomes more skewed.\", \"For a one-way table with $\\\\var{groupsFalse}$ groups, $df = \\\\var{dfFalse}$.\", \"If $\\\\chi^2 = \\\\var{Chi2small}$ with $df = 5$, you reject H$_0$ at the $5\\\\%$ significance level.\", \"If $\\\\chi^2 = \\\\var{Chi2large}$ with $df = 5$, you cannot reject H$_0$ at the $5\\\\%$ significance level.\", \"For a $\\\\var{nRows}\\\\times\\\\var{nCols}$ two-way table, $df=\\\\var{RowsColsProd}$.\", \"A one-way table describes counts for combinations of outcomes for two variables.\", \"A two-way table describes counts for each outcome in a single variable.\", \"When finding the p-value of a chi-square test, we consider the area in the left tail only.\", \"The chi-square test is appropriate for numerical data.\" ]", "description": "", "templateType": "list of strings", "can_override": false}, "choices": {"name": "choices", "group": "Statements", "definition": "shuffle(0..len(statements)-1)[0..6]", "description": "", "templateType": "anything", "can_override": false}, "df": {"name": "df", "group": "Statements", "definition": "(nRows-1)*(nCols-1)", "description": "", "templateType": "anything", "can_override": false}, "statement_marks": {"name": "statement_marks", "group": "Statements", "definition": "map([2,0],x,t_statements)+map([0,2],x,f_statements)", "description": "", "templateType": "anything", "can_override": false}, "RowsColsProd": {"name": "RowsColsProd", "group": "Statements", "definition": "nRows*nCols", "description": "", "templateType": "anything", "can_override": false}, "groupsTrue": {"name": "groupsTrue", "group": "Statements", "definition": "random(3..9)", "description": "Number of groups, true statement.
", "templateType": "anything", "can_override": false}, "groupsFalse": {"name": "groupsFalse", "group": "Statements", "definition": "random(3..9)", "description": "Number of groups, false statement.
", "templateType": "anything", "can_override": false}, "dfTrue": {"name": "dfTrue", "group": "Statements", "definition": "groupsTrue-1", "description": "Number of degrees of freedom, true statement.
", "templateType": "anything", "can_override": false}, "dfFalse": {"name": "dfFalse", "group": "Statements", "definition": "groupsFalse", "description": "Number of degrees of freedom, false statement.
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