1. 15 points JKEStat11 11.E.056. My Notes Ask Your Teacher The psychology depart
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1. 15 points JKEStat11 11.E.056. My Notes Ask Your Teacher The psychology department at a certain college claims that the grades in its introductory course are distributed as follows: 10% As, 22% Bs, 31% Cs, 20% Ds, and 17% Fs. In a poll of 200 randomly selected students who had completed this course, it was found that 16 received As; 41, Bs; 60, Cs; 45, Ds; and 38, Fs. Does this sample contradict the department's claim at the 05 level (a) Find the test statistic. (Give your answer correct to two decimal places.) (i) Find the p-value. (Give your answer bounds exactly.) pExplanation / Answer
Pearsonian chi-sq is given by sum_{i=1}^{5}ci/di ,where c_i=(n_i-E[n_i])^2,d_i=E[n_i] , and under H0,E[n_i]=n*p_i,n=200 for the model,and there are 5 classes,so i runs from 1 to 5,p_i's are proportion given by the department.For instance,for 1st class(A),n_i=16,found by survey,and p_i=0.1,claimed by department.so,for A category,E[n_i]=200*0.1=20 and by result,the chi-sq statistics has 4 degrees of freedom
a) The test statistics value is 2.16
b) From table,the p-value is 0.706
c)as p-value>0.05,we cant reject the null hypothesis so the departments claim cant be contradicted. So,option (ii) will be correct. (not enough evidence to contradict departments claim)
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