Question: Robust Statistics The two-sample t test for comparing population means when the variances are equal is a robust statistical procedure. If the population variances are different, as long as the underlying populations are normal and the sample sizes are equal, then the hypothesis test is still very reliable. Generate a random sample of size 25 from a normal distribution with mean μ1 = 100 and standard deviation σ1 = 5. Generate a second random sample of size 25 from a normal distribution with mean μ2 = 100 and standard deviation σ2 = 5. Conduct a two-sided, two-sample t test for comparing population means assuming the population variances are equal and with a = 0.05. Do this 100 times and record the number of times you reject the null hypothesis. Repeat the same procedure but use σ2 = 7. Record the number of times you reject the null hypothesis. Repeat the same procedure for σ₂ = 10, 15, 20, 25, 30, 50. Use your results to explain the robust nature of this hypothesis test.