Question

Notice that Carlos's observed proportion is 2.99% above the center of the null distribution. Suppose you use computer tochnology to simulate results under the null hypothesis. Atter 3000 simulations, you find that: 195 of the 3000 simulations foll more than 2.99% below the center of the null distribution, and 205 of the 3000 simulations fell more than 2.99% above the center of the null distribution. Use the results of the simulation to calculate the p-value for Carlos's test. p-value = 4. Chip works for a similar communications company that services fural areas in the South. Using the same hypothesis test, Chip uses survey results from his area of the country and calculates a p-value of 0.2517 . Based on his p-value of 0.2517 , Chip has null model a good fit for his observed results.

Answer 1

The p-value for Carlos's test is calculated as 0.1333 by combining the proportions from the simulations. Chip's p-value of 0.2517 indicates that his null model is a good fit for his observed results, as the probability is not sufficiently low to warrant rejecting the null hypothesis.

Step-by-step explanation:

The student is working with the concept of a p-value in the context of hypothesis testing. The p-value represents the probability of obtaining a result at least as extreme as the observed one, assuming that the null hypothesis is true.

To calculate the p-value for Carlos's test using the simulation results provided, you combine the proportions of simulations that fell more than 2.99% below and above the center of the null distribution: (195 + 205) / 3000 = 400 / 3000 = 0.1333. Hence, the p-value is 0.1333.

In Chip's case, a p-value of 0.2517 suggests that there's a 25.17% probability of seeing a result as extreme as his if the null hypothesis is true, which indicates that the null model is a relatively good fit for his observed results. This is because the p-value is not small enough to strongly suggest rejecting the null hypothesis at common significance levels (e.g., 0.05 or 0.01).