Hypothesis Testing Using One Sample
Burkett86
cf_hypothesis_tester_single_sample1.xlsxMean, Sigma Known
| Inputs -- | |||||
| Hypothesized Population Mean: | 295 | <-- Input the appropriate number for your situation | |||
| Population Standard Deviation (sigma): | 12 | <-- Input the appropriate number for your situation | |||
| Sample size (n): | 50 | <-- Input the appropriate number for your situation | |||
| Sample Mean (X-bar) | 297.6 | <-- Input the appropriate number for your situation | |||
| Intermediate Calculations -- | |||||
| Standard Error of the Estimate: | 1.6970562748 | ||||
| Test Statistic (z): | 1.5320646926 | ||||
| Results -- | For the Alpha level given, H0 should be | ||||
| Alpha: | 0.01 | 0.05 | 0.1 | ||
| One tailed, H0: Mu =>295, p= | 0.9372 | not rejected | not rejected | not rejected | |
| One tailed, H0: Mu <=295, p= | 0.0628 | not rejected | not rejected | Rejected | |
| Two-tailed, H0: Mu = 295, p = | 0.1255 | not rejected | not rejected | not rejected |
Hypothesis test for a Population Mean, Sigma Known If the population standard deviation is known, we can directly calculate the standard deviation of the sampling distribution (the standard error of the estimate), and use the standardized normal distribution to get a z multiple, using the Excel function NORMSINV. We can then calculate p for each of the three possible test conditions, and compare it to each level of alpha to see whether the null hypothesis should be rejected.
Mean, Sigma Unknown
| Inputs -- | |||||
| Hypothesized Population Mean: | 7 | <-- Input the appropriate number for your situation | |||
| Sample Standard Deviation (s): | 1.05 | <-- Input the appropriate number for your situation | |||
| Sample size (n): | 60 | <-- Input the appropriate number for your situation | |||
| Sample Mean (X-bar) | 7.25 | <-- Input the appropriate number for your situation | |||
| Intermediate Calculations -- | |||||
| Standard Error of the Estimate: | 0.1355544171 | ||||
| Test Statistic (t): | 1.8442777839 | ||||
| Degrees of Freedom (d.f.): | 59 | ||||
| Results -- | For the Alpha level given, H0 should be | ||||
| Alpha: | 0.01 | 0.05 | 0.1 | ||
| One tailed, H0: Mu =>7, p= | 0.9649 | not rejected | not rejected | not rejected | |
| One tailed, H0: Mu <=7, p= | 0.0351 | not rejected | Rejected | Rejected | |
| Two-tailed, H0: Mu = 7, p = | 0.0702 | not rejected | not rejected | Rejected |
Hypothesis test for a Population Mean, Sigma Unknown If the population standard deviation is not known, we must use the sample standard deviation as an estimate and use it to calculate the standard deviation of the sampling distribution (the standard error of the estimate). We also use the t distribution to get a multiple corresponding to the desired confidence level, using the Excel function TINV. We can then calculate p for each of the three possible test conditions, and compare it to each level of alpha to see whether the null hypothesis should be rejected.
Proportion
| Inputs: | |||||
| Hypothesized population proportion: | 0.35 | <-- Input the appropriate number for your situation | |||
| Sample Proportion (p-bar) | 0.4 | <-- Input the appropriate number for your situation | |||
| Sample Size (n) | 30 | <-- Input the appropriate number for your situation | |||
| Intermediate Calculations: | |||||
| Standard Error of the Estimate: | 0.0871 | ||||
| Test statistic (z): | 0.5741692518 | ||||
| Results: | For the Alpha level given, H0 should be: | ||||
| Alpha: | 0.01 | 0.05 | 0.1 | ||
| One tailed, H0: P => 0.35, p = | 0.7171 | not rejected | not rejected | not rejected | |
| One tailed, H0: P <= 0.35, p = | 0.2829 | not rejected | not rejected | not rejected | |
| Two-tailed, H0: P = 0.35, p = | 0.5659 | not rejected | not rejected | not rejected | |
Hypothesis Tester – Single Sample Hypothesis test for a population proportion From a sample proportion, we can calculate the standard deviation of the sampling distribution (the standard error of the estimate) and use the standardized normal distribution to get a z multiple, using the Excel function NORMSINV. We can then calculate p for each of the three possible test conditions and compare it to each level of alpha to see whether the null hypothesis should be rejected.
