Z-test for the Mean for Comparing Two Samples Null Hypothesis -= Level of Significance First Sample Sample Mean for First Sample Population Standard Deviation for First Sample Sample Size for First Sample Second Sample Sample Mean for Second Sample Population Standard Deviation for Second Sample Sample Size for Second Sample Pooled Variance Z Test Statistic 0 0.05 Enter estimated population mean Enter level of significance 1.05 1.23 50 Enter sample mean for the first s Enter population standard deviat Enter sample size for the first sa 1.23 4.77 5.02 2.1360497 -0.084268 Enter sample mean for the secon Enter population standard deviat Enter sample size for the second Two Tailed Test Lower Critical Value Upper Critical Value p Value Do not reject the null hypothesis -1.959964 1.959964 0.9328436 Lower Tail Test Lower Critical Value p Value Do not reject the null hypothesis -1.644854 0.4664218 Upper Tail Test Upper Critical Value p Value Do not reject the null hypothesis 1.6448536 0.5335782 Use "Descriptive Statistics or Ave sample mean and standard devia Enter estimated population mean Enter level of significance Enter sample mean for the first sample Enter population standard deviation for first sample Enter sample size for the first sample Enter sample mean for the second sample Enter population standard deviation for second sample Enter sample size for the second sample Use "Descriptive Statistics or Average and STDEV functions if sample mean and standard deviation not known t-test for the Mean for Comparing Two Samples with the Same Variance Null Hypothesis -= Level of Significance Population #1 Sample Sample Mean Sample Size Sample Standard deviation Population #2 Sample Sample Mean Sample Size Sample Standard deviation Population 1 Sample Degrees of Freedom Population 2 Sample Degrees of Freedom Total Degrees of Freedom Pooled Variance Difference in Sample Means t-Test Statistic 0 0.05 27.461 10 4.44 25.269 12 2.68 9 11 20 12.82144 2.192 1.429721 Two Tailed Test Lower Critical Value Upper Critical Value p Value Do not reject the null hypothesis -2.085963 2.085963 0.168233 Lower Tail Test Lower Critical Value p Value Do not reject the null hypothesis -1.724718 0.915883 Upper Tail Test Upper Critical Value p Value Do not reject the null hypothesis 1.724718 0.084117 Calculations Area For One Tailed Tests TDIST Value 0.084117 1-TDST Value 0.915883 Enter estimated population mean Enter level of significance Enter sample mean for the first sample Enter sample size for the first sample Enter sample standard deviation for first sample Enter sample mean for the second sample Enter sample size for the second sample Enter sample standard deviation for second sample Use "Descriptive Statistics or Average and STDEV functions if sample mean and standard deviation not known t-test for the Mean for Comparing Two Samples with Different Variances Null Hypothesis -= Level of Significance Population #1 Sample Sample Mean Sample Size Sample Standard deviation Population #2 Sample Sample Mean Sample Size Sample Standard deviation Total Degrees of Freedom (Welch's Rule) Total Degrees of Freedom (Quick Rule) Difference in Sample Means t-Test Statistic 0 0.05 Enter estimated populatio Enter level of significance 133.994 16 11.015 Enter sample mean for th Enter sample size for the Enter sample standard de 138.018 13 12.663 24 12 -4.024 -0.901647 Enter sample mean for th Enter sample size for the Enter sample standard de Two Tailed Test Lower Critical Value Upper Critical Value p Value Do not reject the null hypothesis -2.063899 2.063899 0.376204 Lower Tail Test Lower Critical Value p Value Do not reject the null hypothesis -1.710882 0.188102 Upper Tail Test Upper Critical Value p Value Do not reject the null hypothesis 1.710882 0.811898 Use "Descriptive Statistics sample mean and standa Calculations Area For One Tailed Tests TDIST Value 0.188102 1-TDST Value 0.811898 Enter estimated population mean Enter level of significance Enter sample mean for the first sample Enter sample size for the first sample Enter sample standard deviation for first sample Enter sample mean for the second sample Enter sample size for the second sample Enter sample standard deviation for second sample Use "Descriptive Statistics or Average and STDEV functions if sample mean and standard deviation not known t-test for the Mean for Comparing Paired Samples Null Hypothesis Level of Significance Sample Size Mean Differences Sample Standard Deviation Total Degrees of Freedom t-Test Statistic -= 0 0.05 10 -240 327.2783 9 -2.318964 Enter estimated pop Enter level of signifi Enter the number o Enter the mean diffe Use the calculations deviation and sam Two Tailed Test Lower Critical Value Upper Critical Value p Value Reject the null hypothesis -2.262157 2.262157 0.045563 Lower Tail Test Lower Critical Value p Value Reject the null hypothesis Upper Tail Test Upper Critical Value p Value Do not reject the null hypothesis -1.833113 0.022782 1.833113 0.977218 1 2 3 Calculations Area 4 For One Tailed Tests 5 TDIST Value 0.022782 6 1-TDST Value 0.977218 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Enter estimated population mean Enter level of significance Enter the number of pairs (from Calculation area) Enter the mean difference (from Calculation area) Use the calculations area to enter data and calculate the mean, standard deviation and sample size. Note you can enter up to 25 pairs in this area. Calculation Area Data Before After Difference 5500 6000 -500 1000 900 100 2500 2500 0 7800 8300 -500 6400 6200 200 8800 9400 -600 600 500 100 3300 3500 -200 4500 5200 -700 6500 6800 -300 -240 327.2783389 10 z-test for the Differences in Two Proportions Hypothesized Difference 1 - 2 = Level of Significance Group 1 Number of Successes Sample Size Group 2 Number of Successes Sample Size Group 1 Proportion Group 2 Proportion Difference in the Two Proportions Average Proportion z-test Statistic Normaility Test np = n(1-p) = np = n(1-p) = 0 0.01 Enter the Level of Significance 57 2325 Enter the number of successes for Group 1 Enter the sample size for Group 1 97 2081 0.024516 0.046612 -0.022096 0.034952 -3.986832 Enter the number of successes for Group 2 Enter the sample size for Group 2 57 2268 97 1984 Two Tailed Test Lower Critical Value Upper Critical Value p Value Reject the null hypothesis -2.575829 2.575829 6.70E-005 Lower Tail Test Lower Critical Value p Value Reject the null hypothesis -2.326348 3.35E-005 Upper Tail Test Upper Critical Value p Value Do not reject the null hypothesis 2.326348 0.999967 vel of Significance mber of successes for Group 1 mple size for Group 1 mber of successes for Group 2 mple size for Group 2 = F-Test for Differences in Variances Hypothesized Variance Difference Level of Significance = Population 1 Sample Sample Size Sample Standard Deviation Population 2 Sample Sample Size Sample Standard Deviation F-Test Statistic Population 1 Sample Degrees of Freedom Population 2 Sample Degrees of Freedom 0 0.05 Enter Level of Significance 25 3.02 Enter Sample Size for first sample Enter Sample Standard Deviation for first sample 25 2.14 1.991528 24 24 Enter Sample Size for second sample Enter Sample Standard Deviation for second sam Two Tailed Test Lower Critical Value Upper Critical Value p Value Do not reject the null hypothesis 0.440669 2.269277 0.098115 Lower Tail Test Lower Critical Value p Value Do not reject the null hypothesis 0.504093 0.950943 Upper Tail Test Upper Critical Value p Value Reject the null hypothesis 1.98376 0.049057 Calculations Area FDIST value 0 1-FDIST value 1 e for first sample ndard Deviation for first sample e for second sample ndard Deviation for second sample