Correction on 9.73 Statistics on Large Sample Tests of Hypotheses?
1. The problem statement, all variables and given/known data
(I forgot to write out the problem statement in previous post) How do California H.S. students compare to students nationwide in their college readiness, as measured by their SAT scores? The national average scores for the class of 2003 were 507 on the verbal portion and 519 on the math portion. Suppose that 100 California students from the class of 2003 were randomly selected and their SAT scores recorded as: Verbal: Sample average = 499, Sample standard dev = 98 Math: Sample average = 516, Sample standard dev = 96 a. Do the data provide sufficient evidence to indicate that the average verbal score for all California students in the class of 2003 different from the national average? Test using alpha = .05.is different from the national average? Test using alpha = .05. b. Do the data provide sufficient evidence to indicate that the average math score for all California students in the class of 2003 is different from the national average? Test using alpha = .05. c. Could you use this data to determine if there is a difference between the average math and verbal scores for all California students in the class of 2003? Explain your answer. 2. Relevant equations Relevant DATA: n = 100 (California students sampled) national average scores for verbal = 507 sample California average for verbal = 499 standard dev California for verbal = 98 Relevant EQUATION: SE = standard dev/sqrt(n) z = [sample California average  mean National] [standard dev Californial for verbal/sqrt(n)] OR z = [sample California average  mean National]/ SE 3. The attempt at a solution Since, standard dev of california sample for verbal test = 98 and n = 100 samples SE = standard dev/sqrt(n) = 98/sqrt(100) = 9.8 Thus z = [mean of sample California  mean of National (Popn)]/SE = [499507]/9.8 = 8/9.8 =  0.816 This answer for part a. is wrong. Answers at the back of the book: a. yes; z = 3.33 b. no; z = 1 c. no I am stuck at part a. My wrong answer is z = 0.816. The back of the book says z = 3.33. Please show me how stepbystep to derive at the correct answer. Thank you very much. I get the same answer of z = 0.816 instead of 3.33. I am only concerned about getting the z value because how can I answer yes or no, without knowing it. Also, it is asking for us to test using alpha = .05. Ztest is the only test that seems to apply here since we were are comparing a sample (California) from a population (National). The text book is expecting students to know which tests (ztest, ttest, etc) to solve the problem. Also, the back of the book even says z = 3.33 
Book's answer for part a is wrong on two accounts. You should use a t test; and the answer isn't yes. The reason for using a t test is because the standard deviation is not known, but estimated from the sample. In this case, the "z" statistic in fact follows a t distribution. However, with a large sample size (e.g. n > 30), the t distribution becomes close enough to the standard normal distribution that the z test can be used.

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