Oszacowywanie wartości prawdopodobieństwa z symulacji

An employee at an aquarium monitors how much their sea otters eat. The amount of food a particular otter eats daily is approximately normally distributed with a mean of $17$17 pounds and a standard deviation of $1$1 pound. They suspected this otter was not eating enough, so they took a random sample $n=10$n, equals, 10 days and observed a sample mean of $\bar x=16.5$x, with, \bar, on top, equals, 16, point, 5 pounds of food per day.

To see how likely a sample like this was to occur by random chance alone, the employee performed a simulation. They simulated $40$40 samples of $n=10$n, equals, 10 values from a normal population with a mean of $17$17 pounds and a standard deviation of $1$1 pound. They recorded the mean of the values in each sample. Here are the sample means from their $40$40 samples:

They want to test $H_0: \mu=17 \text{ lbs}$H, start subscript, 0, end subscript, colon, mu, equals, 17, start text, space, l, b, s, end text vs. $H_\text{a}: \mu<17 \text{ lbs}$H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 17, start text, space, l, b, s, end text where $\mu$mu is the true mean amount of food per day.