If false explain why A t-test is used to test the null hypothesis of H_0: mu_1 =

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. We use F test to examine the equality of means for more than 2 groups. t test will be used for testing equality of 2 group means.

2. False. As the assumption of equal variance is there.

3. True as we see a pattern in the residual plot. hence it is not a good fit.

4. False. Power of a test is (1- Probability(Type II error)).

5.True where Not guilty is null hypothesis.

6. False. We have to test the equality in mean lifetime for the 3 brands. Hence it is 1-way ANOVA and not a 2-way as the only factor is brand.

7. True.

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