Python统计代写｜Bonus Assignment: Simulating experiments

Questions & Tasks

In order to complete the tasks below, you will need the following packages:

Task 1: Write a function called t_two_sample which (1) has two input arguments: yA and yB, and which (2) calculates the t-value for a two-sample test.

Task 2: Use your t_two_sample function to verify the t value reported for the dataset above ( $t=2.177$ ).

Task 3: Use scipy.stats.t.sf to verify the p value reported for the dataset above ( $p=0.022$ ).

Task 4: Simulate at least 1000 two-sample experiments to numerically verify the reported p value ( $p=0.022$ ).

Hints:

• See Lesson 09 for examples of experiment simulations.
• For each experiment, use your t_two_sample function (above) to calculate the two-sample t value.
• Also use:
  • $n_{\text{A}}=n_{\text{B}}=10$ (sample size)
  • ${\mu }_{\text{A}}={\mu }_{\text{B}}=0$ (means when $H_0$ is true)
  • ${\sigma }_{\text{A}}={\sigma }_{\text{B}}=1$ (true SD values)
  • $N\ge 1000$ (number of experiments)

• When simulating experiments, ensure that you use the Normal distribution (np.random.randn) and NOT the Uniform distribution (np.random.rand)