Problem 1 (12 points, one point for each). Indicate if a statement is true or fa
ID: 3312677 • Letter: P
Question
Problem 1 (12 points, one point for each). Indicate if a statement is true or false (1) A set of sample means is more likely to result in rejection of the hypothesis of equal population means if the variability within the populations is smaller (2) If every observation is multiplied by 2, then the value of the F statistic in an ANOVA is multiplied by 4 (3) The logarithmic transformation is used when the variance is proportional to the mean (4) To apply the F test in ANOVA, the sample size for each factor level (population) must be the same (5) To apply the F test for ANOVA, the population standard deviations for all factor levels must be the same (6) A "statistically significant F" in an ANOVA indicates that you have identified which levels of factors are different from the others Statements from (7) to (12) should be answered based on the following ANOVA table Sum of Squares 810 720 Degrees of Freedom Source Between Factors Within (error) (7) The null hypothesis is that all four means are equal (8) The calculated value of F is 1.125 (9) The critical value for F for 5% significance is 6.60 (10) The null hypothesis can be rejected at 5% significance (11) The null hypothesis cannot be rejected at 1% significance (12) There are 10 observations in the experimentExplanation / Answer
1.TRUE. The null hypothesis will be reject when the variance "between" the populations is more.
2.TRUE. The F-statistic considers the sum of square values so increasing the observations by factor 2 increases the F-statistic by 4.
3.FALSE. If the variance is proportional to the mean, square root transformation is preferred.
4. FALSE. This is not a necessary condition. The sample sizes for each factor can be different.
5.TRUE. It is a prerequisite in an ANOVA test that the population have the same variance/standard deviation.
6. FALSE. A significant f-test only tells us that at least one pair of the treatment means are different it does not tell us which treatments differ from each other.
7. TRUE.The null hypothesis is always the no difference hypoyhesis.
8.FALSE. The value of F is (810/2)/(720/8) = 405/90 =4.5
9. FALSE. The critical value of F at 5% level of significance and 2,8 degrees of freedom is 4.45897011.
10. TRUE. Since, F-statistic value>F-significant value at 5% significance level.
11. TRUE. The critical value at 1% level of significance for 2,8 degrees of freedom is 8.64911064, therefore, F-statistic value<F-significant value at 1% significance level. So, null hypothesis is accepted.
12. FALSE. There are 11 responses because the total degrees of freedom is always n-1, so here n-1=10 therefore, n=10+1=11.
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