# CHI-squared Test Example for df = 3 at α = 0.01 Solved example work with steps, formula & summary to estimate χ²-statistic (χ²0), critical (table) value (χ²e) for given degrees of freedom & hypothesis test (H0) at a stated level of significance (α = 0.01) for observed frequencies O = {95, 35, 75 & 25} & expected frequencies E = {110, 56, 70 & 23} to check if the result of this probability & statistics experiment is statistically significant.
Calculation Summary
Observed Frequency (O){95, 35, 75 & 25}
Expected Frequency (E){110, 56, 70 & 23}
Significance Level (α)0.01
χ²010.4515
χ²e11.345

## Workout for O = {95, 35, 75 & 25} & E = {110, 56, 70 & 23}

The below is the solved example with step by step calculation shows how to estimate the chi-squared statistic (χ²0), critical (table) value (χ²e) for degrees of freedom & hypothesis test (H0) at a stated level of significance (α = 0.01) for observed frequencies O = {95, 35, 75 & 25} & expected frequencies E = {110, 56, 70 & 23} to check the quality of variances between two or more samples which are not uniformly distributed, may help learners or grade school students to solve the similar chi-squared test (χ²0, χ²e & H0) worksheet problems efficiently.

Workout :
step 1 Address the formula input parameters and values
observed frequency = 95, 35, 75 & 25
expected frequency = 110, 56, 70 & 23
Significance Level (α) = 0.01

step 2 Refer the below χ² table to find χ²-statistic (χ²0)

χ² = ∑(Oi - Ei)2Ei

 Observed Frequency (O) Expected Frequency (E) (O - E)2 (O - E)2E 95 110 225 2.0455 35 56 441 7.875 75 70 25 0.3571 25 23 4 0.1739 ∑(O - E)2E = 10.4515
χ²0 = 10.4515

step 3 Find the degrees of freedom
df = n - 1
df = 4 - 1
df = 3

step 4 Find the critical value of χ²e for df = 3 at a stated level of significance α = 0.01 from χ²-distribution table.
χ²e = 11.345

Inference
for χ²0 < χ²e
There is no significance difference between sample and population
since χ²0 = 10.4515 is smaller than χ²e = 11.345.
Therefore the null hypothesis H0 is accepted. 