Many casinos use card-dealing machines to deal cards at random. occasionally, the machine is tested to ensure an equal likelihood of dealing for each suit. to conduct the test, 1,500 cards are dealt from the machine, while the number of cards in each suit is counted. theoretically, 375 cards should be dealt from each suit. as you can see from the results in the table, this is not the case:

spades diamonds clubs hearts
observed 402 358 273 467
expected 375 375 375 375

with a significance level of .05, test the null hypothesis that the discrepancies are not statistically significant.

part a: what is the degrees of freedom?