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## Statistics and probability

### Course: Statistics and probability>Unit 12

Lesson 1: The idea of significance tests

# 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 $n=10$ days and observed a sample mean of $\overline{x}=16.5$ 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 $n=10$ 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 vs. 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 .