CHI-squared Test Example for df = 3 at α = 0.01
Solved example work with steps, formula and summary to estimate χ²-statistic (χ²0), critical (table) value (χ²e) for given degrees of freedom and hypothesis test (H0) at a stated level of significance (α = 0.01) for observed frequencies O = {95, 35, 75 & 25} and expected frequencies E = {110, 56, 70 & 23} to check if the result of this probability and 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 |
| χ²0 | 10.4515 |
| χ²e | 11.345 |
Workout for O = {95, 35, 75 & 25} and 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 and hypothesis test (H0) at a stated level of significance (α = 0.01) for observed frequencies O = {95, 35, 75 & 25} and 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 students and learners solve similar chi-squared test (χ²0, χ²e and 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
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.
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 | |||
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.
