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The types of raw materials used to construct stone tools found at the archaelogical site Casa del Rito are shown below. A random sample of 1486 stone tools was obtained from a current excavation site.

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I'm trying to run a Chi-squared goodness of fit test on this data. Here is a table of my calculations:

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Now I use the formula

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And get $\chi^2=.1829$

The answer key says I should have $\chi^2=.1984$

Anyone see anything I might have done wrong? Or maybe the answer key is wrong?

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    A couple of things could be going on. 1) There is a minor error in the tabular data, since the total number of tools is 1487 rather than 1486. 2) I cannot get the same result as you, which may be due to rounding errors on your part? 3) I also cannot get the same answer as the referenced answer key. – String Nov 08 '21 at 07:48
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    Also, in principle your calculations look fine - but avoid rounding off multiple times along the way in case you have done that, since rounding errors can accumulate. – String Nov 08 '21 at 07:49

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