True and false question If false explain why? A t-test is used to test the null

Question

True and false question

If false explain why?

A t-test is used to test the null hypothesis of H_0: mu_1 = mu_2 = mu_3 = mu_4 = 0 A Wilcoxon Rank Sum test is used to test a null hypothesis of H_0: mu_1 - mu_2 = 17 if the assumption of equal variances is not satisfied. Suppose we are doing regression analysis and we fit a straight line to the data. We test the assumption of equal variances and end up with the residual plot below. This indicates that the chosen model is not a good fit. The power of a test is the probability of making a type 2 error Person is judged not guilty when they did commit the crime (letting a guilty person go free) is an example of type 2 error Three different brands of automobile batteries, each one having 42-month warranty, were included in a study of battery lifetime. A random sample of batteries of each brand was selected and lifetime (in months) was determined, resulting in the following data. This should be tested with a 2WAY ANOVA with the factors being Brand and Lifetime. Suppose you are doing a 2-Facor ANOVA with both fixed effects. You first check the interaction and it is significant (there is an interaction). You now need to test the main effects (each factor) to see if there is a significant difference between the treatments for each factor. If you find there is a difference, you use Tukey's simultaneous intervals to determine where the significant differences are.

Explanation / Answer

1) False. If there are more than 2 means, you cannot use t-test. Use one way anova or a non parametric test.

2) True. When equality of variances is not satisfied, Wilcoxon test is applicable.

3) True. In the Predicted vs Residual plot, a good model would form a Horizontal Band around zero. For the values over zero, we see a quadratic pattern suggesting variances are not equal.

4) False. Power of test is probability of not committing type II error

5) True/ Type 2 error is rejecting alternate hypothesis when it's true. In this case, letting guilty person go.

6) False. We only need to do a one way anova and test for difference in mean across the 3 bands.

7) True. This is std procedure for testing effects.

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