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ISM Chapter 14

# ISM Chapter 14 - Chapter 14 14.1 Equal-variances t-test of...

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Chapter 14 14.1 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 This Year 3 Years Ago Mean 8.29 10.36 Variance 8.13 8.43 Observations 100 100 Pooled Variance 8.28 Hypothesized Mean Difference 0 df 198 t Stat -5.09 P(T<=t) one-tail 0.0000 t Critical one-tail 1.6526 P(T<=t) two-tail 0.0000 t Critical two-tail 1.9720 t = –5.09, p-value = 0. There is overwhelming evidence to conclude that there has been a decrease over the past three years. 14.2 a z-test of 2 1 p p - (case 1) 0 ) p p ( : H 2 1 0 = - 0 ) p p ( : H 2 1 1 - + - - = 2 1 2 1 n 1 n 1 ) p ˆ 1 ( p ˆ ) p ˆ p ˆ ( z 1 2 3 4 5 6 7 A B C D E z-Test of the Difference Between Two Proportions (Case 1) Sample 1 Sample 2 z Stat 2.83 Sample proportion 0.4336 0.2414 P(Z<=z) one-tail 0.0024 Sample size 113 87 z Critical one-tail 1.6449 Alpha 0.05 P(Z<=z) two-tail 0.0047 z Critical two-tail 1.9600 61

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z = 2.83, p-value = .0024. There is enough evidence to infer that customers who see the ad are more likely to make a purchase than those who do not see the ad. b 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 Ad No Ad Mean 97.38 92.01 Variance 621.97 283.26 Observations 49 21 Pooled Variance 522.35 Hypothesized Mean Difference 0 df 68 t Stat 0.90 P(T<=t) one-tail 0.1853 t Critical one-tail 1.6676 P(T<=t) two-tail 0.3705 t Critical two-tail 1.9955 t = .90, p-value = .1853. There is not enough evidence to infer that customers who see the ad and make a purchase spend more than those who do not see the ad and make a purchase. c z-estimator of p n ) p ˆ 1 ( p ˆ z p ˆ 2 / - ± α 1 2 3 4 5 6 A B C D E z-Estimate of a Proportion Sample proportion 0.4336 Confidence Interval Estimate Sample size 113 0.4336 0.0914 Confidence level 0.95 Lower confidence limit 0.3423 Upper confidence limit 0.5250 ± We estimate that between 34.23% and 52.50% of all customers who see the ad will make a purchase. d t-estimator of μ n s t x 2 / α ± 62
1 2 3 4 5 6 7 A B C D t-Estimate: Mean Ad Mean 97.38 Standard Deviation 24.94 LCL 90.22 UCL 104.55 We estimate that the mean amount spent by customers who see the ad and make a purchase lies between \$90.22 and \$104.55. 14.3 t-test of D μ 0 : H D 0 = μ 0 : H D 1 μ 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 Before After Mean 381.00 373.12 Variance 39001 40663 Observations 25 25 Pearson Correlation 0.96 Hypothesized Mean Difference 0 df 24 t Stat 0.70 P(T<=t) one-tail 0.2438 t Critical one-tail 1.7109 P(T<=t) two-tail 0.4876 t Critical two-tail 2.0639 t = .70, p-value = .2438. There is not enough evidence to conclude that the equipment is effective. 14.4 a z-test of p : H 0 p = .95 : H 1 p > .95 n ) p 1 ( p p p ˆ z - - = 63

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1 2 3 4 5 6 7 8 9 10 11 A B C D z-Test: Proportion Prority Sample Proportion 0.9714 Observations 245 Hypothesized Proportion 0.95 z Stat 1.54 P(Z<=z) one-tail 0.0619 z Critical one-tail 1.6449 P(Z<=z) two-tail 0.1238 z Critical two-tail 1.9600 z = 1.54, p-value = .0619. There is not enough evidence to infer that the spokesperson's claim is true.
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