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# Estimating P-values from simulations

You might need: Calculator

## Problem

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 pounds and a standard deviation of 1 pound. They suspected this otter was not eating enough, so they took a random sample n, equals, 10 days and observed a sample mean of 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 samples of n, equals, 10 values from a normal population with a mean of 17 pounds and a standard deviation of 1 pound. They recorded the mean of the values in each sample. Here are the sample means from their 40 samples:
They want to test H, start subscript, 0, end subscript, colon, mu, equals, 17, start text, space, l, b, s, end text vs. 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 is the true mean amount of food per day.
Based on these simulated results, what is the approximate p-value of the test?
Note: The sample result was x, with, \bar, on top, equals, 16, point, 5, start text, space, l, b, s, end text.