Specific p-value test

I’m doing a simple homework problem and I don’t believe my own answer. Would really appreciate if someone could point out what I’m doing wrong! I have: H0:mu = 16, H1: mu!=16, sigma = 0.1, n = 9. xbar = 16.09.

I set up my p value as such: probability of xbar happening given mu=16. P( (X-16)/(0.1/3) >= (16.09-16)/(0.1/3) ) = P( T8 >= 2.7 ) = a very small value which makes me therefore reject the null.

However, 16.09 isn’t even a standard deviation away from mu, so there’s no way in hell that the probability of it happening is that small and I’m pretty sure I should NOT reject the null… Where did my calculation go wrong?

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Nevin Manimala

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