Project Blue Book: Analysis of Reports of Unidentified Aerial Objects was published by the U.S. Air Force (Air Technical Intelligence Center at Wright-Patterson Air Force Base) ¡n May 1955 to analyze reports of unidentified flying objects (UFOs). In its Table II, the report classified 1765 sightings later regarded as known objects and 434 sightings later regarded as unknown, according to the object color (nine categories).

The report states: “The chi-square test is applicable only to distributions which have the same number of elements,” so the investigators multiplied all counts in the known category by (434/1765), so each row has 434 observations, before computing X². They reported X² = 26.15 with df = 8. Explain why this is incorrect. What should X² equal?