# Appendix 15 - Appendix 15 A15.1 Chi-squared goodness-of-fit...

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Appendix 15 A15.1 Chi-squared goodness-of-fit test : H 0 50 . p 1 = , 20 . p 2 = , 15 . p 3 = 10 . p 4 = 05 . p 5 = : H 1 At least one i p is not equal to its specified value . - = χ i 2 i i 2 e ) e f ( 1 2 3 4 5 6 7 C D E Actual Expected 183 175 63 70 55 52.5 29 35 20 17.5 p-value= 0.6321 p-value = .6321. There is not enough evidence to conclude that applicants to WLU's MBA program are different in terms of their undergraduate degrees from the population of MBA applicants? A15.2 t-test of D μ D 0 : H μ = 0 D 1 : H μ < 0 D D D D n / s x t μ - = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A B C t-Test: Paired Two Sample for Means First Sat Second SAT Mean 1175 1190 Variance 28422 35392 Observations 40 40 Pearson Correlation 0.91 Hypothesized Mean Difference 0 df 39 t Stat -1.20 P(T<=t) one-tail 0.1182 t Critical one-tail 1.6849 P(T<=t) two-tail 0.2365 t Critical two-tail 2.0227 179

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t = –1.20, p-value = .1182. There is not enough evidence to indicate that repeating the SAT produces higher exam scores. A15.3 Time to solve the 48 problems: Equal-variances t-test of 2 1 μ - μ 0 ) ( : H 2 1 0 = μ - μ 0 ) ( : H 2 1 1 μ - μ + μ - μ - - = 2 1 2 p 2 1 2 1 n 1 n 1 s ) ( ) x x ( t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A B C t-Test: Two-Sample Assuming Equal Variances Diet Not Mean 581.95 551.5 Variance 2716.6 2221.5 Observations 20 20 Pooled Variance 2469.1 Hypothesized Mean Difference 0 df 38 t Stat 1.94 P(T<=t) one-tail 0.0300 t Critical one-tail 1.6860 P(T<=t) two-tail 0.0601 t Critical two-tail 2.0244 t = 1.94, p-value = .0300. There is enough evidence to conclude that dieters take longer to solve the 48 problems than do nondieters. Successfully repeat string of five letters: z-test of 2 1 p p - (case 1) : H 0 2 1 p p - = 0 : H 1 2 1 p p - < 0 + - - = 2 1 2 1 n 1 n 1 ) p ˆ 1 ( p ˆ ) p ˆ p ˆ ( z 180
1 2 3 4 5 6 7 8 9 10 11 A B C D z-Test: Two Proportions Diet Not Sample Proportions 0.50 0.80 Observations 20 20 Hypothesized Difference 0 z Stat -1.99 P(Z<=z) one tail 0.0234 z Critical one-tail 1.6449 P(Z<=z) two-tail 0.0468 z Critical two-tail 1.96 z = –1.99, p-value = .0234. There is enough evidence to conclude that dieters are less successful at repeating string of five letters. Successfully repeat string of five words:

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Appendix 15 - Appendix 15 A15.1 Chi-squared goodness-of-fit...

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