Question

2) A random sample of black bears were weighed at various times of the year. Some of the bears were weighed in the spring, some in the summer and some in the fall. The bears were tagged so that the same bear was not measured more than once. Use a 1% significance level and the following Statcato statistics, graphs and ANOVA printout to test the population claim that the time of year (season) is related to the weight of the bears. One-way ANOVA: Significance level = 0.01 Selected column variables: C1 Spring Bear Weig... C2 Summer Bear Weig... C3 Fall Bear Weight... Source of Variation DOF SS MS Test statistic F Critical value Fp-Value 2 45539.29263 22769.64632 13.55345 5.0472 0.00002 Treatment (Between Groups) Error (Within Groups) 51 85679.46663 1679.98954 Total 53 131218.75926 a) Give the null and alternative hypothesis. b) Check the assumptions for a One-Way ANOVA test. c) Write a sentence to explain the F test statistic. d) Use the F test statistic and Critical Value to determine if the sample data significantly disagrees with the null hypothesis. Explain your answer. e) Use the P-value and Significance Level to answer the following: Could the sample data or more extreme have occurred because of sampling variability or is it unlikely that the sample data occurred because of sampling variability? Explain your answer. f) Should we reject the null hypothesis or fail to reject the null hypothesis? Explain your answer. g) Write a conclusion for the hypothesis test addressing evidence and the claim. h) What is the variance between the groups? What is the variance within the groups? Was the variance between significantly higher than the variance within? Explain how you know, i) Was the categorical and quantitative variables related or not. Explain your answer

Answer 1

(a) The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

(b) To use the ANOVA test we made the following assumptions:

• Each group sample is drawn from a normally distributed population
• All populations have a common variance
• All samples are drawn independently of each other
• Within each sample, the observations are sampled randomly and independently of each other
• Factor effects are additive

The assumptions are met.

(c) The F statistic just compares the joint effect of all the variables together. To put it simply, reject the null hypothesis only if your alpha level is larger than your p-value.

(d) Since 13.55345 > 5.0472, we can reject the null hypothesis.