4. John suspects that students who wear glasses tend to finish exams faster than students without glasses. In order to test this claim, John records the average and standard deviation for the minutes taken to complete an exam in his Stat 151 class. Sample Size Average Standard Deviation Glasses 16 41.4 4 No Glasses 64 45.4 13.86 a. (8 marks) Does the above data provide sufficient evidence to suggest that the Stat 151 students with glasses write exams faster than those without glasses? Test at a significance level of a=0.05. b. (2 marks) Can John claim that these results apply to all individuals? Explain. 5. According to data released by Statistics Canada. In both 2006 and 2011, the percentage of individuals who are fluent in French is greater among individuals living B.C. than those living in Alberta. Specifically, in 2006, 7.3% of the B.C. population was fluent in French vs 6.9% in Alberta; in 2011 6.9% in B.C. vs 6.6% in Alberta. A researcher is interested in testing whether this trend has persisted into present times. Thus, the researcher collects a random sample of 500 individuals from B.C. and a random sample of 500 individuals from Alberta. 35 of the individuals in the B.C. sample report that they are fluent in French, while only 30 of the individuals in the Alberta sample report that they are fluent in French. a. (8 marks) Does this provide evidence that the proportion of French speakers in B.C. is greater than that of Alberta? Test at a 10% significance level. b. (2 marks) Are there any threats to the assumptions needed for this test be be valid? Explain. 6. A horribly jaded statistics instructor is interested in comparing Canadian politicians to U.S. politicians. The instructor collects a random sample consisting of 30 Canadian politicians and 70 U.S. Politicians, and he classifies each politician as one of the following: Liar, Thief, Idiot, Scoundrel. The data are summarized in the following 2-way table