A psychologist runs rats through a maze and records the total time it takes for them to navigate the course.The run times are normally distributed, and we believe the standard deviation of the run times is 121 sec.Calculate the p-value from a test to see if the mean run time differs from 600 sec if 20 randomly sampled rats have an average run time of 583 sec.
A) 0.5286
B) 0.2643
C) 0.7357
D) 0.8883

Question

Quizplus · Accepted Answer

To calculate the p-value for this two-tailed test, we first find the test statistic using the formula for a z-test: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{583 - 600}{121/\sqrt{20}} \approx -0.627$. Looking up the z-score of -0.627 in a standard normal distribution table or using a calculator gives a one-tailed p-value of approximately 0.2643. Since this is a two-tailed test (we're checking if the mean run time differs, which could be either higher or lower), we double the one-tailed p-value: $2 \times 0.2643 = 0.5286$.

A Psychologist Runs Rats Through a Maze and Records the Total