### 4.4 The Chi-squared test for independence.

 Write a hypothesis:Null Hypothesis:             H0: the data sets are independentAlternative Hypothesis:  H1: the data sets are not independent (ie. dependent)Calculate the chi-squared value on the Calulator:Calculator Sheet    => [menu]        => 7: Matrix            => 1: Create                => 1: Matrix                         ~ type in number of columns and rows (TAB is useful for this)                        => [enter]                            ~type in values from table                            => [enter]                                => [ctrl] [var] [A] [enter]                                    => [menu]                                        => 6: Statistics                                            => 7: Stat tests                                                => 8: Chi squared 2-way test                    magic! on your screen will be the chi-squared vale and the p-valueConclusion:Comparing chi-squared valueIf your chi-squared calculated value is less than your chi-squared critical value you accept the null hypothesis.                     chi-squared calculated < chi-squared critical          accept  H0 : the data sets are independentIf your chi-squared calculated value is greater than your chi-squared critical value you reject the null hypothesis and accept the alternative hypothesis.                      chi-squared calculated > chi-squared critical          reject  H0, accept H1 : the data sets are not independent                 chi high, no H0Comparing p-valueIf your p-value is less than your significance level you reject the null hypothesis and accept the alternative hypothesis.                     p-value < significance level             reject  H0, accept H1 : the data sets are not independent                                            P low, no H0If your p-value is greater than your significance level you accept the null hypothesis.                       p-value > significance level          accept  H0 : the data sets are independent