One common way to test for authenticity of data is to analyze the frequencies of digits. When people are weighed and their weights are rounded to the nearest pound, we expect the last digits 0, 1, 2, . . . , 9 to occur with about the same frequency. In contrast, if people are asked how much they weigh, the digits 0 and 5 tend to occur at higher rates. The author randomly selected 80 students, obtained their weights, and recorded only the last digits, with the results shown in the following table. At the 0.01 significance level, test the claim that the last digits occur with the same frequency. Based on the results, does it appear that the students were actually weighed or were they asked to report their weights?
Last digit
0 12 3 4 56789
Frequency
35 0 2 1 4 24 1 4 7 2