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MinitabGuide3 - MINITAB Guide (Chapters 14-22) When...

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Unformatted text preview: MINITAB Guide (Chapters 14-22) When performing a significance test with the subcommand alternative 0 (i.e., two-sided test), MINITAB also produces a confidence interval. To specify the confidence level, need to also submit a confidence subcommand when performing the test. Can combine computation of a confidence interval and performing a significance test when the alternative is two-sided. For left-tail or right-tail alternatives, a confidence interval must be computed separately from performing a significance test. Normal Probability Plot MTB > pplot C1 To draw a normal probability plot for data in C1 using the Menus: 1. Click on Graph → Probability Plot and select the Single plot. Click on OK. 2. Select C1 for the Graph variable. 3. Make sure Distribution is set to Normal. Click on OK. Data Set: Battery_Life (Output using Menu.) Population Mean Population Standard Deviation KNOWN / Summarized Data Confidence Interval (One-Sample Z-Interval) MTB > onez n xbar; SUBC> sigma sig; SUBC> confidence p. Significance Test (One-Sample Z-Test) MTB > onez n xbar; SUBC> sigma sig; SUBC> test mu; SUBC> alternative w. where: n is the sample size. xbar is the sample mean. sig is the population standard deviation. p is the level of confidence (specified as a percent or a proportion). mu is the value (of mean) in null hypothesis. w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) n = 45, x = 63.9 Assume σ = 3.5 90% Confidence Interval MTB > onez 45 63.9; SUBC> sigma 3.5; SUBC> confidence 0.90. One­Sample Z The assumed standard deviation = 3.5 N Mean SE Mean 90% CI 45 63.900 0.522 (63.042, 64.758) Test: H0: μ = 63.7 vs. Ha: μ > 63.7 MTB > onez 45 63.9; SUBC> sigma 3.5; SUBC> test 63.7; SUBC> alternative 1. One­Sample Z Test of mu = 63.7 vs > 63.7 The assumed standard deviation = 3.5 95% Lower N Mean SE Mean Bound Z P 45 63.900 0.522 63.042 0.38 0.351 1 Population Mean Population Standard Deviation KNOWN / Using a Data Set Confidence Interval (One-Sample Z-Interval) MTB > onez cy; SUBC> sigma sig; SUBC> confidence p. Significance Test (One-Sample Z-Test) MTB > onez cy; SUBC> sigma sig; SUBC> test mu; SUBC> alternative w. where: cy is the column containing the sample. sig is the population standard deviation. p is the level of confidence (specified as a percent or a proportion). mu is the value (of mean) in null hypothesis. w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) Data Set: Filling_Bottles Assume σ = 0.04 99% Confidence Interval MTB > onez c1; SUBC> sigma 0.04; SUBC> confidence 99. One­Sample Z: Amount of Juice The assumed standard deviation = 0.04 Variable N Mean StDev Amount of Juice 6 64.0117 0.0422 SE Mean 99% CI 0.0163 (63.9696, 64.0537) Test: H0: μ = 64.05 vs. Ha: μ ≠ 64.05 MTB > onez c1; SUBC> sigma 0.04; SUBC> test 64.05; SUBC> alternative 0. One­Sample Z: Amount of Juice Test of mu = 64.05 vs not = 64.05 The assumed standard deviation = 0.04 Variable N Mean StDev Amount of Juice 6 64.0117 0.0422 SE Mean 95% CI Z P 0.0163 (63.9797, 64.0437) ­2.35 0.019 n = 7, x = 1.38 , s = 0.29 95% Confidence Interval MTB > onet 7 1.38 0.29; SUBC> confidence 95. One­Sample T N Mean StDev SE Mean 95% CI 7 1.380 0.290 0.110 (1.112, 1.648) Test: H0: μ = 2 vs. Ha: μ < 2 MTB > onet 7 1.38 0.29; SUBC> test 2; SUBC> alternative ­1. One­Sample T Test of mu = 2 vs < 2 95% Upper N Mean StDev SE Mean Bound 7 1.380 0.290 0.110 1.593 T P ­5.66 0.001 Population Mean Population Standard Deviation UNKNOWN / Summarized Data Confidence Interval (One-Sample t-Interval) MTB > onet n xbar s; SUBC> confidence p. Significance Test (One-Sample t-Test) MTB > onet n xbar s; SUBC> test mu; SUBC> alternative w. where: n is the sample size. xbar is the sample mean. s is the sample standard deviation. p is the level of confidence (specified as a percent or a proportion). mu is the value (of mean) in null hypothesis. w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) 2 Population Mean Population Standard Deviation UNKNOWN / Using a Data Set Confidence Interval (One-Sample t-Interval) MTB > onet cy; SUBC> confidence p. Significance Test (One-Sample t-Test) MTB > onet cy; SUBC> test mu; SUBC> alternative w. where: cy is the column containing the sample. s is the sample standard deviation. p is the level of confidence (specified as a percent or a proportion). mu is the value (of mean) in null hypothesis. w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) Data Set: Battery_Life 90% Confidence Interval MTB > onet c1; SUBC> confidence 90. One­Sample T: BattLife Variable N Mean StDev BattLife 10 9.470 2.141 SE Mean 90% CI 0.677 (8.229, 10.711) Test: H0: μ = 10 vs. Ha: μ > 10 MTB > onet c1; SUBC> test 10; SUBC> alternative 1. One­Sample T: BattLife Test of mu = 10 vs > 10 Variable N Mean StDev SE Mean BattLife 10 9.470 2.141 0.677 95% Lower Bound T P 8.229 ­0.78 0.773 Data Set: Water_Clarity 98% Confidence Interval MTB > paired c2 c3; SUBC> confidence 98. Paired T­Test and CI: Initial, 5 Years Later Paired T for Initial ­ 5 Years Later N Mean StDev SE Mean Initial 6 50.33 10.99 4.49 5 Years Later 6 53.75 12.73 5.20 Difference 6 ­3.42 4.04 1.65 98% CI for mean difference: (­8.96, 2.13) T­Test of mean difference = 0 (vs not = 0): T­Value = ­2.07 P­Value = 0.093 Test: H0: μ1 = μ2 vs. Ha: μ1 < μ2 MTB > paired c2 c3; SUBC> alternative ­1. Paired T­Test and CI: Initial, 5 Years Later Paired T for Initial ­ 5 Years Later N Mean StDev SE Mean Initial 6 50.33 10.99 4.49 5 Years Later 6 53.75 12.73 5.20 Difference 6 ­3.42 4.04 1.65 95% upper bound for mean difference: ­0.10 T­Test of mean difference = 0 (vs < 0): T­Value = ­2.07 P­Value = 0.046 Difference of Two Population Means Two DEPENDENT Samples (Matched Pairs) Confidence Interval (Paired-Sample t-Interval) MTB > paired cx cy; SUBC> confidence p. Significance Test (Paired-Sample t-Test) MTB > paired cx cy; SUBC> test mu. where: cx (sample 1) and cy (sample 2) are the columns containing the two samples. p is the level of confidence (specified as a percent or a proportion). w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) Alternative way to compute confidence intervals and significance tests for match paired data is to: 1) Compute a column of differences. For example, if match paired data is in c2 and c3, then: MTB > let c4 = c2 – c3 2) Apply one-sample t procedures (i.e., MINITAB command onet ) to these differences. 3 Difference of Two Population Means Two INDEPENDENT Samples / Summarized Data Confidence Interval (Two-Sample t-Interval) MTB > twot n1 x1 s1 n2 x2 s2; SUBC> confidence p. Significance Test (Two-Sample t-Test) MTB > twot n1 x1 s1 n2 x2 s2; SUBC> alternative w. where: n1, x1, s1 are the sample size, sample mean, and standard deviation for the first sample. n2, x2, s2 are the sample size, sample mean, and standard deviation for the second sample. p is the level of confidence (specified as a percent or a proportion). w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) Sample 1: n = 40, x = 7.8 , s = 3.3 Sample 2: n = 50, x = 11.6 , s = 2.6 95% Confidence Interval and Test: H0: μ1 = μ2 vs. Ha: μ1 ≠ μ2 MTB > twot 40 7.8 3.3 50 11.6 2.6; SUBC> alternative 0; SUBC> confidence 95. Two­Sample T­Test and CI Sample N Mean StDev SE Mean 1 40 7.80 3.30 0.52 2 50 11.60 2.60 0.37 Difference = mu (1) ­ mu (2) Estimate for difference: ­3.800 95% CI for difference: (­5.072, ­2.528) T­Test of difference = 0 (vs not =): T­Value = ­5.95 P­Value = 0.000 DF = 73 Difference of Two Population Means Two INDEPENDENT Samples / Samples in Two Columns Confidence Interval (Two-Sample t-Interval) MTB > twosample cx cy; SUBC> confidence p. Significance Test (Two-Sample t-Test) MTB > twosample cx cy; SUBC> alternative w. where: cx (sample 1) and cy (sample 2) are the columns containing the two samples. p is the level of confidence (specified as a percent or a proportion). w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) Data Set: Bacteria 99% Confidence Interval MTB > twosample c1 c2; SUBC> confidence 99. Two­Sample T­Test and CI: Carpeted, Uncarpeted Two­sample T for Carpeted vs Uncarpeted N Mean StDev SE Mean Carpeted 8 11.20 2.68 0.95 Uncarpeted 8 9.79 3.21 1.1 Difference = mu(Carpeted)­mu(Uncarpeted) Estimate for difference: 1.41 99% CI for difference: (­3.04, 5.86) T­Test of difference = 0 (vs not =): T­Value = 0.96 P­Value = 0.357 DF =13 Test: H0: μ1 = μ2 vs. Ha: μ1 > μ2 MTB > twosample c1 c2; SUBC> alternative 1. Two­Sample T­Test and CI: Carpeted, Uncarpeted Two­sample T for Carpeted vs Uncarpeted N Mean StDev SE Mean Carpeted 8 11.20 2.68 0.95 Uncarpeted 8 9.79 3.21 1.1 Difference= mu (Carpeted)­mu(Uncarpeted) Estimate for difference: 1.41 95% lower bound for difference: ­1.20 T­Test of difference = 0 (vs >): T­Value = 0.96 P­Value = 0.178 DF = 13 4 Difference of Two Population Means Data Set: Bacteria Two INDEPENDENT Samples / Samples “Stacked” in Single Column Confidence Interval (Two-Sample t-Interval) MTB > twot cx cy; SUBC> confidence p. Significance Test (Two-Sample t-Test) MTB > twot cx cy; SUBC> alternative w. where: cx is the column containing the two samples. cy is the column containing the sample indicator variable. p is the level of confidence (specified as a percent or a proportion). w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) 99% Confidence Interval MTB > twot c5 c4; SUBC> confidence 99. Test: H0: μ1 = μ2 vs. Ha: μ1 > μ2 MTB > twot c5 c4; SUBC> alternative 1. n = 200, No. of Successes = 102 92% Confidence Interval MTB > pone 200 102; SUBC> confidence 92; SUBC> usez. Test and CI for One Proportion Sample X N Sample p 1 102 200 0.510000 92% CI (0.448116, 0.571884) Using the normal approximation. Test: H0: p = 0.6 vs. Ha: p < 0.6 MTB > pone 200 102; SUBC> test 0.6; SUBC> alternative ­1; SUBC> usez. Test and CI for One Proportion Test of p = 0.6 vs p < 0.6 95% Upper Sample X N Sample p Bound 1 102 200 0.510000 0.568143 Z­Value P­Value ­2.60 0.005 Using the normal approximation. Population Proportion Summarized Data Confidence Interval (One-Sample z-Interval) MTB > pone n x; SUBC> confidence p; SUBC> usez. Significance Test (One-Sample z-Test) MTB > pone n x; SUBC> test pi; SUBC> alternative w; SUBC> usez. where: n the sample size. x is the number of successes. p is the level of confidence (specified as a percent or a proportion). pi is the value (of population proportion) in null hypothesis. w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) 5 Population Proportion Using a Data Set Confidence Interval (One-Sample z-Interval) MTB > pone cy; SUBC> confidence p; SUBC> usez. Significance Test (One-Sample z-Test) MTB > pone cy; SUBC> test pi; SUBC> alternative w; SUBC> usez. where: cy is the column containing the sample. (This will be a column of two different symbols.) p is the level of confidence (specified as a percent or a proportion). pi is the value (of population proportion) in null hypothesis. w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) Data Set: Voting 95% Confidence Interval MTB > pone c1; SUBC> confidence 0.95; SUBC> usez. Test and CI for One Proportion: VoteRep Event = Y Variable X N Sample p VoteRep 53 100 0.530000 95% CI (0.432178, 0.627822) Using the normal approximation. Test: H0: p = 0.5 vs. Ha: p ≠ 0.5 MTB > pone c1; SUBC> test 0.5; SUBC> alternative 0; SUBC> usez. Test and CI for One Proportion: VoteRep Test of p = 0.5 vs p not = 0.5 Event = Y Variable X N Sample p VoteRep 53 100 0.530000 95% CI Z­Value P­Value (0.432178, 0.627822) 0.60 0.549 Using the normal approximation. Sample 1: n = 100, No. of successes = 55 Sample 2: n = 200, No. of successes = 80 95% Confidence Interval and Test: H0: p1 = p2 vs. Ha: p1 ≠ p2 MTB > ptwo 100 55 200 80; SUBC> alternative 0; SUBC> pooled; SUBC> confidence 95. Test and CI for Two Proportions Sample X N Sample p 1 55 100 0.550000 2 80 200 0.400000 Difference = p (1) ­ p (2) Estimate for difference: 0.15 95% CI for difference: (0.0311835, 0.268817) Test for difference = 0 (vs not = 0): Z = 2.46 P­Value = 0.014 Fisher's exact test: P­Value = 0.019 Difference of Two Population Proportions Summarized Data Confidence Interval (Two-Sample z-Interval) MTB > ptwo n1 x1 n2 x2; SUBC> confidence p. Significance Test (Two-Sample z-Test) MTB > ptwo n1 x1 n2 x2; SUBC> alternative w; SUBC> pooled. where: n1, x1 are the sample size and number of successes for the first sample. n2, x2 are the sample size and number of successes for the second sample. p is the level of confidence (specified as a percent or a proportion). w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) 6 Difference of Two Population Proportions Data in Two Columns Confidence Interval (Two-Sample z-Interval) MTB > ptwo cx cy; SUBC> confidence p. Significance Test (Two-Sample z-Test) MTB > ptwo cx cy; SUBC> alternative w; SUBC> pooled. where: cx (sample 1) and cy (sample 2) are the columns containing the two samples. p is the level of confidence (specified as a percent or a proportion). w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) Data Set: Survey 90% Confidence Interval MTB > ptwo c1 c2; SUBC> confidence 90. Test and CI for Two Proportions: Current, Former Event = Y Variable X N Sample p Current 73 120 0.608333 Former 86 120 0.716667 Difference = p (Current) ­ p (Former) Estimate for difference: ­0.108333 90% CI for difference: (­0.208083, ­0.00858327) Test for difference = 0 (vs not = 0): Z = ­1.79 P­Value = 0.074 Fisher's exact test: P­Value = 0.101 Test: H0: p1 = p2 vs. Ha: p1 < p2 ptwo c1 c2; SUBC> alternative ­1; SUBC> pooled. Test and CI for Two Proportions: Current, Former Event = Y Variable X N Sample p Current 73 120 0.608333 Former 86 120 0.716667 Difference = p (Current) ­ p (Former) Estimate for difference: ­0.108333 95% upper bound for difference: ­0.00858327 Test for difference = 0 (vs < 0): Z = ­1.77 P­Value = 0.038 Fisher's exact test: P­Value = 0.051 7 Difference of Two Population Proportions Samples “Stacked” in Single Column Confidence Interval (Two-Sample z-Interval) MTB > ptwo cx cy; SUBC> stacked; SUBC> confidence p. Significance Test (Two-Sample z-Test) MTB > ptwo cx cy; SUBC> stacked; SUBC> alternative w; SUBC> pooled. where: cx is the column containing the two samples. cy is the column containing the sample indicator variable. p is the level of confidence (specified as a percent or a proportion). w defines the sign in alternative hypothesis: ­1 is for the left­tail Ha (< alternative) 0 is for the two­sided Ha (≠ alternative) 1 is for the right­tail Ha (> alternative) Data Set: Survey 90% Confidence Interval MTB > ptwo c5 c4; SUBC> stacked; SUBC> confidence 90. Test: H0: p1 = p2 vs. Ha: p1 < p2 MTB > ptwo c5 c4; SUBC> stacked; SUBC> alternative ­1; SUBC> pooled. P­value for test statistic = 18.738 and df = 5 (i.e., 6 categories). MTB > cdf 18.738 k1; SUBC> chisq 5. MTB > let k2=1­k1 MTB > print k2 Data Display K2 0.00215047 2 Chi-Square P-Value: P( Χ 2 > Χ 0 ) MTB > cdf x k1; SUBC> chisq df. MTB > let k2=1­k1 MTB > print k2 where: x is the value of the test statistic. df is the degrees of freedom, which equals the number of categories minus 1. k2 equals the P­value. 8 ...
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This note was uploaded on 03/05/2011 for the course STAT 350 taught by Professor Sims,r during the Spring '08 term at George Mason.

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