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) This is false, as in t test we just compare 2 groups. Here 4 groups are mentioned. Anova test will be appropriate here.

2) This is true. If we are unable to meet the parametric assumptions of a t-test, we can use Wilcoxon rank sum test, or more commonly known as Mann-Whitney U test.

3) This is true. The model is not a good fit as it violates the assumption of equal variances or homoscedasticity. If this assumption is met then points should form a random band around a horizontal line.

4) This is false. The power of a hypothesis test is 1 minus the probability of a Type 2 error.

5) This is true. This is a case of failing to reject the null hypothesis when null hypothesis should have been rejected.

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