Statistics Help : Hypothesis Testing

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SUMMARY

The discussion focuses on the nuances of hypothesis testing, specifically regarding the selection of integer values in statistical calculations. A participant questions the choice of using 16 instead of 17 when determining P(X>=16) in relation to a significance level of 0.005. The consensus suggests that rounding should favor more conservative estimates, as demonstrated by the comparison of probabilities 0.0064 and 0.0021, with the former being closer to the desired significance level. The importance of adhering to established norms in statistical practices is emphasized.

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TL;DR
There's this question and I have worked it out until the end but don't understand why the answer is the answer
1595814004874.png

Answer :
1595814030267.png

I understnad why x(< or = ) 2 but I do not understand why we use 16 instead of 17 for the second range? When P(X>=16) > 0.005(which is the level of significance). Thank you for all the help given :)
 

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"As close as possible to 0.005".

0.0064 is closer to 0.0050 than 0.0021.
 
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None of this is exact of course but I believe I was taught to default to the more conservative number when rounding to an integer value. This is not what the question prescribes but seems more prudent to me ( the significance level will be 1% or less). I am not sure which is the norm!
 
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