Hypothesis Tester - Single Sample 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. Inputs: Hypothesized population mean: 295 Population standard deviation (sigma): 12 Sample size (n): 50 Sample mean (x-bar): 297.6 <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. Intermediate Calculations: Standard error of the estimate: 1.69705627 Test statistic (z): 1.53206469 Results: One-tailed, H0: Mu =>295, p= 0.9372 For the Alpha level given, H0 should be: 0.01 Not rejected One-tailed, H0: Mu <=295, p= 0.0628 Not rejected Two-tailed, H0: Mu = 295, p = 0.1255 Not rejected Alpha: End of worksheet ate number for your situation. ate number for your situation. ate number for your situation. ate number for your situation. he Alpha level given, H0 should be: 0.05 Not rejected 0.1 Not rejected Not rejected Rejected Not rejected Not rejected Hypothesis Tester - Single Sample 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. Inputs: Hypothesized population mean: 7 Sample standard deviation (s): 1.05 Sample size (n): 60 Sample mean (x-bar): 7.25 <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. Intermediate Calculations: Standard error of the estimate: 0.1355544 Test statistic (t): 1.8442778 Degrees of freedom (d.f.): 59 Results: One-tailed, H0: Mu =>7, p= 0.9649 End of worksheet For the Alpha level given, H0 should be: Alpha: 0.01 0.05 Not rejected Not rejected One tailed, H0: Mu <=7, p= 0.0351 Not rejected Rejected Two-tailed, H0: Mu = 7, p = 0.0702 Not rejected Not rejected our situation. our situation. our situation. our situation. H0 should be: 0.1 Not rejected Rejected 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. Inputs: Hypothesized population proportion: 0.35 Sample proportion (p-bar): 0.4 Sample size (n): 30 <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. Intermediate Calculations: Standard error of the estimate: 0.0871 Test statistic (z): 0.5741692518 Results: One tailed, H0: P => 0.35, p = 0.7171 For the Alpha level given, H0 should b 0.01 Not rejected One tailed, H0: P <= 0.35, p = 0.2829 Not rejected Two-tailed, H0: P = 0.35, p = 0.5659 Not rejected Alpha: End of worksheet te number for your situation. te number for your situation. te number for your situation. he Alpha level given, H0 should be: 0.05 Not rejected 0.1 Not rejected Not rejected Not rejected Not rejected Not rejected Running head: HYPOTHESIS TESTING 1 Hypothesis Testing 1 Michelle Mc Donald- Upshaw MBA-FP6018 December 11, 2016 Professor: Jeffrey Edwards 1 HYPOTHESIS TESTING 1 2 Hypothesis Testing 1 Practical Application Scenario Playbill Magazine Chief Operating Officer, In the year 2010 Boos Allen consultants suggested that we increase the price of our magazine. Due to the over whelming impact that this could have on the bottom-line of the magazine another survey was requested of Boos Allen in 2012. In the most recent sample taken we discovered that the standard deviation of household income from 2010 to 2012 was unchanged. The mean annual household income increased from $119,155 to $124,450 respectively (Capella University, n.d.). By using the MS-Excel template we will test the claim to determine if the annual household income increase then the price of the magazine should also increase. The Null Hypothesis will assume the opposite of the test we are conducting that the household income has not increased (Capella University, n.d.). The Alternative Hypothesis states income has increased. If Playbill finds enough evidence to support this then an increase is justified. However, if this evidence is absent we can assume that mean income did not increase. Hypothesized population mean: Population standard deviation (sigma): Sample size (n): Sample mean (x-bar): 119,155 30,000 300 124,450 Intermediate Calculations: Standard error of the estimate: Test statistic (t): Degrees of freedom (d.f.): 1732.0508 1 3.0570696 8 299 Results: Alpha For the Alpha level given, H0 should be: Mu < = $119,155 0.01 0.05 0.1 HYPOTHESIS TESTING 1 3 : One-tailed, H0: Mu =>7, p= 0.9988 Not rejected Not rejected One tailed, H0: Mu <=119155, p= 0.0012 Rejected Rejected Rejecte Two-tailed, H0: Mu = 119155, p = 0.0024 Rejected Rejected Rejecte The data above indicates that the Null Hypothesis which states that the household income did not increase should be rejected as the p-value is less for all levels. With these results I recommend an increase in price for the subscription of Playbill Magazine. This recommendation can ultimately increase revenue for the company without an impact in subscriptions. If the alpha was .01 the increase is still my recommendation as the household income will still be rejected. Not rejec HYPOTHESIS TESTING 1 4 References Capella University. (n.d.). Hypothesis Tester- Single Sample. Retrieved from Capella University, MBA-FP6018