Using the F-distribution is a natural candidate because the test statistic is the ratio of two scaled sums of squares each of which follows a scaled chi-squared distribution.
jˈuːzɪŋ ðɪ ˈɛfdˌɪstɹɪbjˈuːʃən ɪz ɐ nˈætʃɚɹəl kˈændᵻdˌeɪt bɪkˈʌz ðə tˈɛst stɐtˈɪstɪk ɪz ðə ɹˈeɪʃɪˌoʊ ʌv tˈuː skˈeɪld sˈʌmz ʌv skwˈɛɹz ˈiːtʃ əv wˌɪtʃ fˈɑːloʊz ɐ skˈeɪld kˈaɪskwˈɛɹd dˌɪstɹɪbjˈuːʃən.