A fisher caught 20 fish. Let the distribution of the weights of the fish be normal, with unknown mean $\mu$ and standard deviation $\sigma =1.2$ pounds. The sample of 20 fish had an average weight of 3.45 pounds.
I want to calculate the p-value to test $H_0:\mu=3$ against $H: \mu\ne 3$. But I'm somewhat confused: do I need to find the probability that $D\ge 3$ and $D<3$? (Where $D=\frac{|3.45-3|}{1.2/\sqrt{20}}$) in this case). Also, I think I need to use the T-distribution here, correct?
I think my understanding is incorrect. Would appciate some advice.
Yes, you are correct. We need to use the T-distribution here, as the sample size is not large (large meaning $\geq 30$).
Now, the value of D is calculated as $1.677$. Finding, $$P = P (T <1.677) \approx 0.05$$
Hence, we do not reject $H_0$ (or, we accept $H_0$).