The senior executives of CareFree Insurance, Inc.feel that "a minority of our employees perceive an authoritarian management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis.Eighty employees rate the management as authoritarian.Using $\alpha$ = 0.05, the observed value of chi-square is ___.

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The chi-square statistic is calculated as:$\chi^2 = \frac{(O - E)^2}{E}$where O is the observed frequency and E is the expected frequency.In this case, the expected frequency for each category is 100 (since there are 200 employees in the sample and we are testing a hypothesis about the proportion of employees who perceive an authoritarian management style).Therefore, the chi-square statistic is:$\chi^2 = \frac{(80 - 100)^2}{100} + \frac{(120 - 100)^2}{100} = 8.00$

The Senior Executives of CareFree Insurance, Inc α\alphaα = 005, the Observed Value of Chi-Square Is ___

The Senior Executives of CareFree Insurance, Inc $\alpha$ = 005, the Observed Value of Chi-Square Is ___