8 MCQs in Statistics ...

13. The biologists trying to predict the spring fox population are trying to find the best set of predictors. The researchers hypothesized about what might make good predictors and then collected data. The following table summarizes these results Predictor Variable (s) Adjusted R^2 Fall Rabbit Population 0.889 Fall Rabbit and vole Population 0.956 Fall Rabbit and bird Population 0.875 Fall Ball Population 0.501 Based on the information provided, which set of variables provided the best predictor of the spring fox population? (Points: 5) Fall rabbit population Fall rabbit and vole populations Fall rabbit and bird population Fall vole population 

11. The heights of 40 randomly selected people and the heights of their mothers are recorded. Statdisk is used to run a linear correlation and regression analysis. The partial results are provided below: Sample size, n 40 Degrees of freedom: 38 Correlation Results: Correlation coeff, r: 0.6033907 Critical r: +-0.3120061 P-value (two tailer): 0.00004 Reject the Null Hypothesis Based on the hypothesis test, what can be concluded? (Points: 5) There is insufficient evidence to conclude that there is a linear correlation between a person’s height and the height of his/her mother. There is sufficient evidence to conclude that there is a linear correlation between a person’s height and the height of his/her mother. There is sufficient evidence to conclude that scatter plot of the population would follow a horizontal line. The hypothesis test indicates that we should use the father’s heights instead of mother’s heights. 

15. Raccoons are sampled and weighed from three different neighborhoods. Using a 0.05 significance level what can you conclude from the following ANOVA results? Source: DF: SS: MS: Test Stat F: Critical F: P-Value Treatment: 2 78.545455 39.272727 3.043682 3.315826 0.062588 Error: 30 387.090909 12.90303 Total: 32 465.636364 There is sufficient evidence to conclude that at least one group of raccoons has a different mean weight than the other groups. There is insufficient evidence to conclude that at least one group of raccoons has a different mean weight than the other groups. We reject the null hypothesis. Both (a) and (c) 

16. Raccoons are identified by gender and then weighed from three different neighborhoods. Using a 0.05 significance level what can you conclude from the following Two-Way ANOVA results? Source: DF: SS: MS: TEST STAT F: CRITICAL F: P-VALUE: Interaction: 2 4.2 2.1 0.33 3.4028 0.7235 Gender: 1 145.2 145.2 22.6875 4.2597 0.0001 Neighborhood 2 178.8667 89.4333 13.9740 3.4028 0.0001 Doing a two-way ANOVA would be inappropriate because there is sufficient evidence of an interaction between gender and neighborhood. There is sufficient evidence to conclude that raccoons vary in weight by gender. There is sufficient evidence to conclude that raccoons vary in weight by neighborhood. Both (b) and (c) 

17. Suppose that you wish to test the effect of lowering the soil ph on the number of lady ferns in an area. The researchers hypothesize that lowering the ph-level of the soil will lead to more ferns. Several plots of forest are randomly chosen and the number of lady ferns counted, before and after the soil has been treated with lime (which lowers the soil ph). Before Treatment 10 20 13 30 After Treatment 8 15 14 30 Using the sign test, what can be concluded from this experiment? (Points: 5) We do not reject the null hypothesis. We reject the null hypothesis. There is no evidence that treating the soil with lime increases the number of ferns. Both (a) and (c) 

18. Researchers wish to determine if there is a difference between the median home selling price and list price. A random sample of 50 homes is chosen (their selling and list prices are recorded) and the Wilcoxon Signed-Rank Test is performed. Statdisk returns the following information: Num Unequal pairs: 49 Using Approximation Test Statistic, T: 0.0000 Mean, u: 612.5 St Dev: 100.5298 Test Statistic, z: -6.0927 Critical z: +-1.959962 Based upon this output, what can be concluded about the median home selling and list prices? There is sufficient evidence to conclude that there is a difference in the median home selling and list prices. There is insufficient evidence to conclude that there is a difference in the median home selling and list prices. The results are statistically insignificant. Both (b) and (c) 

19. We wish to test if there is a difference in the median weights for yellow and brown M&M’s. A random sample of both types of M&M’s is selected and weighed. The data was analyzed in Statdisk and with the following results. Total Num Values: 59 Rank sum 1: 829.5000 Rank sum 2: 940.5000 Mean, u: 780 St Dev: 65.49809 Test Statistic, z: 0.7557 Critical z: +-1.959962 Fail to reject the Null Hypothesis. Of these two choices (Wilcoxon signed-rank for matched pairs or Wilcoxon signed-rank for two independent samples) what type of test should have been conducted? What can be concluded? (Points: 5) The Wilcoxon signed-rank for matched pairs should have been conducted. There is insufficient evidence to conclude that there is a difference in the median weight of yellow and brown M&M’s. The Wilcoxon signed-rank for two independent samples should have been conducted. There is insufficient evidence to conclude that there is a difference in the median weight of yellow and brown M&M’s. The Wilcoxon signed-rank for matched pairs should have been conducted. There is sufficient evidence to conclude that there is a difference in the median weight of yellow and brown M&M’s. The Wilcoxon signed-rank for two independent samples should have been conducted. There is sufficient evidence to conclude that there is a difference in the median weight of yellow and brown M&M’s. 

20. Consumer Reports scored cars on quality and cost. Spearman’s rank correlation coefficient was calculated using Statdisk and the output is provided below. Based on these results, does quality appear to be associated with price? What was the sample size used? Sample size, n: 10 Correlation Coeff, r: 0.5636 Critical r: +-0.648 Fail to Reject the Null Hypothesis There is sufficient evidence to conclude that the quality and price of a car are associated. We cannot determine sample size from the output displayed. There is insufficient evidence to conclude that the quality and price of a car are associated. We cannot determine sample size from the output displayed. There is sufficient evidence to conclude that the quality and price of a car are associated. There were ten cars used in the sample. There is insufficient evidence to conclude that the quality and price of a car are associated. There were ten cars used in the sample.