Statistics For Decision Making W5 *Excel*
z-test
| Z-test for the Mean for Comparing Two Samples | |||||
| Null Hypothesis μ - µ = | 0 | Enter estimated population mean | |||
| Level of Significance | 0.05 | Enter level of significance | |||
| First Sample | |||||
| Sample Mean for First Sample | 1.05 | Enter sample mean for the first sample | |||
| Population Standard Deviation for First Sample | 1.23 | Enter population standard deviation for first sample | |||
| Sample Size for First Sample | 50 | Enter sample size for the first sample | |||
| Second Sample | |||||
| Sample Mean for Second Sample | 1.23 | Enter sample mean for the second sample | |||
| Population Standard Deviation for Second Sample | 4.77 | Enter population standard deviation for second sample | |||
| Sample Size for Second Sample | 5.02 | Enter sample size for the second sample | |||
| Pooled Variance | 2.1360496715 | ||||
| Z Test Statistic | -0.0842677033 | Use "Descriptive Statistics or Average and STDEV functions if | |||
| sample mean and standard deviation not known | |||||
| Two Tailed Test | |||||
| Lower Critical Value | -1.9599639845 | ||||
| Upper Critical Value | 1.9599639845 | ||||
| p Value | 0.9328435901 | ||||
| Do not reject the null hypothesis | |||||
| Lower Tail Test | |||||
| Lower Critical Value | -1.644853627 | ||||
| p Value | 0.466421795 | ||||
| Do not reject the null hypothesis | |||||
| Upper Tail Test | |||||
| Upper Critical Value | 1.644853627 | ||||
| p Value | 0.533578205 | ||||
| Do not reject the null hypothesis |
t-test - var the same
| t-test for the Mean for Comparing Two Samples with the Same Variance | |||||
| Null Hypothesis μ - µ = | 0 | Enter estimated population mean | |||
| Level of Significance | 0.05 | Enter level of significance | |||
| Population #1 Sample | |||||
| Sample Mean | 27.461 | Enter sample mean for the first sample | |||
| Sample Size | 10 | Enter sample size for the first sample | |||
| Sample Standard deviation | 4.44 | Enter sample standard deviation for first sample | |||
| Population #2 Sample | |||||
| Sample Mean | 25.269 | Enter sample mean for the second sample | |||
| Sample Size | 12 | Enter sample size for the second sample | |||
| Sample Standard deviation | 2.68 | Enter sample standard deviation for second sample | |||
| Population 1 Sample Degrees of Freedom | 9 | ||||
| Population 2 Sample Degrees of Freedom | 11 | Use "Descriptive Statistics or Average and STDEV functions if | |||
| Total Degrees of Freedom | 20 | sample mean and standard deviation not known | |||
| Pooled Variance | 12.82144 | ||||
| Difference in Sample Means | 2.192 | ||||
| t-Test Statistic | 1.4297214412 | ||||
| Two Tailed Test | |||||
| Lower Critical Value | -2.0859634473 | ||||
| Upper Critical Value | 2.0859634473 | Calculations Area | |||
| p Value | 0.1682331032 | For One Tailed Tests | |||
| Do not reject the null hypothesis | TDIST Value | 0.0841165516 | |||
| 1-TDST Value | 0.9158834484 | ||||
| Lower Tail Test | |||||
| Lower Critical Value | -1.7247182429 | ||||
| p Value | 0.9158834484 | ||||
| Do not reject the null hypothesis | |||||
| Upper Tail Test | |||||
| Upper Critical Value | 1.7247182429 | ||||
| p Value | 0.0841165516 | ||||
| Do not reject the null hypothesis |
t-test - var different
| t-test for the Mean for Comparing Two Samples with Different Variances | |||||
| Null Hypothesis μ - µ = | 0 | Enter estimated population mean | |||
| Level of Significance | 0.05 | Enter level of significance | |||
| Population #1 Sample | |||||
| Sample Mean | 133.994 | Enter sample mean for the first sample | |||
| Sample Size | 16 | Enter sample size for the first sample | |||
| Sample Standard deviation | 11.015 | Enter sample standard deviation for first sample | |||
| Population #2 Sample | |||||
| Sample Mean | 138.018 | Enter sample mean for the second sample | |||
| Sample Size | 13 | Enter sample size for the second sample | |||
| Sample Standard deviation | 12.663 | Enter sample standard deviation for second sample | |||
| Total Degrees of Freedom (Welch's Rule) | 24 | ||||
| Total Degrees of Freedom (Quick Rule) | 12 | Use "Descriptive Statistics or Average and STDEV functions if | |||
| Difference in Sample Means | -4.024 | sample mean and standard deviation not known | |||
| t-Test Statistic | -0.901646849 | ||||
| Two Tailed Test | |||||
| Lower Critical Value | -2.0638985616 | ||||
| Upper Critical Value | 2.0638985616 | ||||
| p Value | 0.3762044287 | Calculations Area | |||
| Do not reject the null hypothesis | For One Tailed Tests | ||||
| TDIST Value | 0.1881022144 | ||||
| Lower Tail Test | 1-TDST Value | 0.8118977856 | |||
| Lower Critical Value | -1.7108820799 | ||||
| p Value | 0.1881022144 | ||||
| Do not reject the null hypothesis | |||||
| Upper Tail Test | |||||
| Upper Critical Value | 1.7108820799 | ||||
| p Value | 0.8118977856 | ||||
| Do not reject the null hypothesis |
paired t-test
| t-test for the Mean for Comparing Paired Samples | ||||||||
| Null Hypothesis μ - µ = | 0 | Enter estimated population mean | ||||||
| Level of Significance | 0.05 | Enter level of significance | ||||||
| Sample Size | 10 | Enter the number of pairs (from Calculation area) | ||||||
| Mean Differences | -240 | Enter the mean difference (from Calculation area) | ||||||
| Sample Standard Deviation | 327.2783388969 | |||||||
| Total Degrees of Freedom | 9 | Use the calculations area to enter data and calculate the mean, standard | ||||||
| t-Test Statistic | -2.318963855 | deviation and sample size. Note you can enter up to 25 pairs in this area. | ||||||
| Two Tailed Test | Calculation Area | |||||||
| Lower Critical Value | -2.2621571628 | Data | ||||||
| Upper Critical Value | 2.2621571628 | Before | After | Difference | ||||
| p Value | 0.0455630295 | 1 | 5500 | 6000 | -500 | |||
| Reject the null hypothesis | 2 | 1000 | 900 | 100 | ||||
| 3 | 2500 | 2500 | 0 | |||||
| Lower Tail Test | Calculations Area | 4 | 7800 | 8300 | -500 | |||
| Lower Critical Value | -1.8331129327 | For One Tailed Tests | 5 | 6400 | 6200 | 200 | ||
| p Value | 0.0227815148 | TDIST Value | 0.0227815148 | 6 | 8800 | 9400 | -600 | |
| Reject the null hypothesis | 1-TDST Value | 0.9772184852 | 7 | 600 | 500 | 100 | ||
| 8 | 3300 | 3500 | -200 | |||||
| Upper Tail Test | 9 | 4500 | 5200 | -700 | ||||
| Upper Critical Value | 1.8331129327 | 10 | 6500 | 6800 | -300 | |||
| p Value | 0.9772184852 | 11 | ||||||
| Do not reject the null hypothesis | 12 | |||||||
| 13 | ||||||||
| 14 | ||||||||
| 15 | ||||||||
| 16 | ||||||||
| 17 | ||||||||
| 18 | ||||||||
| 19 | ||||||||
| 20 | ||||||||
| 21 | ||||||||
| 22 | ||||||||
| 23 | ||||||||
| 24 | ||||||||
| 25 | ||||||||
| -240 | ||||||||
| 327.2783388969 | ||||||||
| 10 |
z-test for the proportion
| z-test for the Differences in Two Proportions | |||||||||
| Hypothesized Difference ρ1 - ρ2 = | 0 | ||||||||
| Level of Significance | 0.01 | Enter the Level of Significance | |||||||
| Group 1 | |||||||||
| Number of Successes | 57 | Enter the number of successes for Group 1 | |||||||
| Sample Size | 2325 | Enter the sample size for Group 1 | |||||||
| Group 2 | |||||||||
| Number of Successes | 97 | Enter the number of successes for Group 2 | |||||||
| Sample Size | 2081 | Enter the sample size for Group 2 | |||||||
| Group 1 Proportion | 0.024516129 | ||||||||
| Group 2 Proportion | 0.0466122057 | ||||||||
| Difference in the Two Proportions | -0.0220960766 | = | |||||||
| Average Proportion | 0.0349523377 | ||||||||
| z-test Statistic | -3.9868320816 | ||||||||
| Normaility Test | |||||||||
| np = | 57 | ||||||||
| n(1-p) = | 2268 | ||||||||
| np = | 97 | ||||||||
| n(1-p) = | 1984 | ||||||||
| Two Tailed Test | |||||||||
| Lower Critical Value | -2.5758293035 | ||||||||
| Upper Critical Value | 2.5758293035 | ||||||||
| p Value | 0.0000669614 | ||||||||
| Reject the null hypothesis | |||||||||
| Lower Tail Test | |||||||||
| Lower Critical Value | -2.326347874 | ||||||||
| p Value | 0.0000334807 | ||||||||
| Reject the null hypothesis | |||||||||
| Upper Tail Test | |||||||||
| Upper Critical Value | 2.326347874 | ||||||||
| p Value | 0.9999665193 | ||||||||
| Do not reject the null hypothesis |
F-test
| F-Test for Differences in Variances | ||||||||||
| Hypothesized Variance Difference | 0 | |||||||||
| Level of Significance α = | 0.05 | Enter Level of Significance | ||||||||
| Population 1 Sample | ||||||||||
| Sample Size | 25 | Enter Sample Size for first sample | ||||||||
| Sample Standard Deviation | 3.02 | Enter Sample Standard Deviation for first sample | ||||||||
| Population 2 Sample | ||||||||||
| Sample Size | 25 | Enter Sample Size for second sample | ||||||||
| Sample Standard Deviation | 2.14 | Enter Sample Standard Deviation for second sample | ||||||||
| F-Test Statistic | 1.9915276443 | |||||||||
| Population 1 Sample Degrees of Freedom | 24 | |||||||||
| Population 2 Sample Degrees of Freedom | 24 | |||||||||
| Two Tailed Test | Calculations Area | |||||||||
| Lower Critical Value | 0.4406689345 | FDIST value | 0.0490573816 | |||||||
| Upper Critical Value | 2.2692772776 | 1-FDIST value | 0.9509426184 | |||||||
| p Value | 0.0981147633 | |||||||||
| Do not reject the null hypothesis | ||||||||||
| Lower Tail Test | ||||||||||
| Lower Critical Value | 0.5040933467 | |||||||||
| p Value | 0.9509426184 | |||||||||
| Do not reject the null hypothesis | ||||||||||
| Upper Tail Test | ||||||||||
| Upper Critical Value | 1.9837595685 | |||||||||
| p Value | 0.0490573816 | |||||||||
| Reject the null hypothesis |