Project part b: Hypothesis testing and confidence intervals, Exams of Statistics

Download Project part b: Hypothesis testing and confidence intervals and more Exams Statistics in PDF only on Docsity! Running Head: Course Project Part- B Running Head: Course Project Part- B HYPOTHESIS QUESTIONS WITH 100% CORRECT ANSWERS 2O23 A hypothesis testing involves the testing of the null hypothesis and the alternative hypothesis. When testing the hypothesis, either the null hypothesis or the alternative hypotheses is rejected. The Company can use hypothesis testing to examine if it should keep a current process, change a current process or start a new process. It can also examine different areas to see if an employee or manager’s ideas would prove more productive. The hypothesis testing can quickly be applied or tested saving the Company time and money. Requirement A: The Average Mean Sales per Week exceeds 41.5 per salesperson. Key Statistics were computed using Minitab Descriptive Statistics: Sales (Y) Variable SALES NUMBER 100 MEAN 42.55 SE MEAN 0.717 7.1708937 ST.DEVIATIO N VARIANCE 5 51.421717 2 Running Head: Course Project Part- B The alternative hypothesis states that mean sales per week exceeds 41.5; this is a one tailed test to the right. The given a = .05 is to the right of Z = 1.645. Therefore, we reject the null hypothesis if the Z > 1.645. If the p value is less than the a = .05 then reject the null hypothesis. Step- 5 Decision Making The 100 salespersons average mean is 42.55. The computed Z score is = 1.464. The computed score is less than 1.645, we do not reject the null hypothesis. We can be 95% confident that the average sales per week will fall within the 95% Confidence Interval (CI) of (41.145, 43.955). The Company can expect a salesperson to achieve sales an average of 42.55 sales a week. Running Head: Course Project Part- B Requirement B: Testing to see if a proportion of salespeople that received online training is less than 55%. Descriptive Statistics: Sales (Y) Variable SALES NUMBER 100 MEAN 42.55 SE MEAN 0.717 7.1708937 ST.DEVI ATION VARIAN CE 5 51.421717 2 MINIMUM 21 Q1 39 MEDIAN 43 Q3 47 MAXIMUM 67 RANGE 46 Descriptive Statistics: Sales (Y) Variab N N* Mean SE StD Minimum Medi Q3 Running Head: Course Project Part- B le Mean ev Q1 an Sales (Y) 50 0 43.840 0.949 6.7 08 29.000 40.000 44.0 00 48.0 00 Varia ble Sales (Y) Maxi mum 67. 000 Uh[] Test and CI for One Proportion: Test of p = 0.55 vs p not = 0.55 Exact Samp le X N Sample p 95% CI P- Value 1 5 0 100 0.500000 (0.3983 21, 0.6016 79) 0.366 Test and CI for One Proportion: Test of p = 0.55 vs p < 0.55 Samp le X N Sample p 95% Upper Bound Exa ct P- Valu e 1 5 0 100 0.500000 0.586 378 0.1 83 Running Head: Course Project Part- B Step 5-Decision Making The online trained salesperson mean is 43.84. The computed, using Minitab, Z score -1.01 and P value of 0.157. The computed Z score is greater than -1.645, do not reject the null hypothesis. We can be 95% confident that the true population mean that received online training will not fall within the Confidence Interval (CI) of (0.3983, 0.6017). The Company can expect that 43.84% of salespersons will have received online training. Running Head: Course Project Part- B Requirement C: The mean number of calls made per week by salespeople that had no training is less than 145. Descriptive Statistics: Calls (X1) CALLS NU MBE R 20 MEAN 140.3 SE MEAN 2.44 ST. DEVIATION10.8923 118.642 VARIANCE 1 MINIMUN 120 Q1 131.75 MEDIAN 141 Q3 145 MAXIMUM 160 RANGE 40 One-Sample T: Calls (X1) Running Head: Course Project Part- B Test of μ = 145 vs ≠ 145 N Mean St-Dev SE Mean 95% CI T P 20 140.30 10.89 2.44 (135.20, 145.40) -1.93 0.069 One-Sample Z: Calls (X1) Test of μ = 145 vs < 145 The assumed standard deviation = 10.89 N Mean SE Mean 95% Upper Bound Z P 20 140.30 2.44 144.31 -1.93 0.027 Step 1- Hypotheses Ho: μ = 145 Ha:μ < 145 Running Head: Course Project Part- B Requirement D: To test the mean time per call to see if it is greater than 15 minutes Descriptive Statistics: Time (X2) Variable NUMBER TIME 100 MEAN 15.3 SE MEAN 0.23 ST.DEVIATION 2.299880541 VARIANCE 5.289450505 MINIMUM 10.0 Q1 13.6 MEDIAN 15.1 Q3 17.075 MAXIMUM 20.0 RANGE 10.0 One-Sample Z: Time (X2) Test of μ = 15 vs > 15 The assumed standard deviation = 2.3 N Mean SE Mean 95% Lower Bound Z P 10 0 15.3 38 0.230 14.960 1.4 7 0.0 71 Running Head: Course Project Part- B One-Sample Z: Time (X2) Test of μ = 15 vs ≠ 15 The assumed standard deviation = 2.3 N Mean SE Mean 95% CI Z P 10 0 15.3 38 0.230 (14.8 87, 15.78 9) 1.4 7 0.1 42 In this scenario, the Z score with single tail test will be used due the same reason as mentioned in first scenario. Step 1- Hypotheses Ho: μ = 15minutes Ha:μ > 15 minutes Running Head: Course Project Part- B Step 2- Level of Significance The a = 0.05 is given. Step 3- Identify the statistical test to use Use z-test because Standard Deviation is known and the sample (n=100) is a large sample (n > 30). This test will be a single tailed test to the right. The computed Z Score Test – Single Tail, to the right, One-Sample Z = 1.47 and P = 0.071 Step 4- Rejection Region The alternative hypothesis states the average time per call is greater than 15 minutes. The given probability of .05 is to the right of Z. Thus, we reject the null hypothesis if Z > 1.645. We accept the alternative hypothesis that the average call time is greater than 15 minutes. Step 5- Decision Making Running Head: Course Project Part- B (X2) Years (X3) 5.000 One-Sample Z: Sales (Y) The assumed standard deviation = 7.17 1 Variable N Mean StDev Sales (Y) 100 42.550 7.171 SE Mea n 0.7 17 95% CI (41.145, 43.955) One-Sample Z: Sales (Y) Test of mu = 41.5 vs > 41.5 The assumed standard deviation = 7.17 1 Variable N Mean StDev SE Mean 95% Lower Bound Z P Sales (Y) 100 42.550 7.171 0.71 7 41.370 1.46 0.0 72 Distribution Plot Normal, Mean=42.55, StDev=7.171 Running Head: Course Project Part- B D en 0.05 0.04 0.03 0.02 0.01 0.05 0.00 42.55 X 54.35 Running Head: Course Project Part- B Appendix- II Descriptive Statistics: Sales (Y), Calls (X1), Time (X2), Years (X3) Variabl e Type N Mean SE Mean StD ev Mini mum Q1 Medi an Sales (Y) GROU P 3 0 42.7 7 1.31 7. 16 31. 00 38.7 5 43.0 0 NONE 2 0 39.3 0 1.89 8. 44 29. 00 35.2 5 37.0 0 ONLI NE 5 0 43.7 20 0.896 6.3 38 21.0 00 41.0 00 44.0 00 Calls (X1) GROU P 3 0 156. 57 2.51 13. 74 131. 00 149. 75 154. 50 NONE 2 0 140. 30 2.44 10. 89 120. 00 131. 25 141. 00 ONLI NE 5 0 173. 70 1.89 13. 38 149. 00 162. 50 174. 00 Time (X2) GROU P 3 0 15.8 53 0.369 2.0 21 12.4 00 14.4 50 15.3 00 NONE 2 0 16.2 90 0.552 2.4 69 10.0 00 14.8 50 16.4 50 ONLI NE 5 0 14.6 48 0.313 2.2 11 10.9 00 13.0 00 14.2 50 Years (X3) GROU P 3 0 2.46 7 0.238 1.3 06 1.0 00 1.00 0 2.00 0 NONE 2 0 2.05 0 0.285 1.2 76 0.0 00 1.00 0 2.00 0 Running Head: Course Project Part- B Test and CI for One Proportion Test of p = 0.55 vs p not = 0.55 Exact Samp le X N Sample p 95% CI P- Value 1 5 0 100 0.500000 (0.3983 21, 0.6016 79) 0.366 Test and CI for One Proportion Test of p = 0.55 vs p < 0.55 Samp le X N Sample p 95% Upper Bound Exa ct P- Valu e 1 5 100 0.586 0.1 Running Head: Course Project Part- B 0 0.500000 378 83 Distribution Plot Normal, Mean=42.55, StDev=6.708 0.06 Running Head: Course Project Part- B D en Distribution Plot Normal, Mean=140.3, StDev=10.89 0.04 0.03 0.02 0.01 0.05 0.00 122.4 140.3 X Running Head: Course Project Part- B Variable Type Maximum Calls (X1) NONE 160.00 One-Sample T: Calls (X1) Test of μ = 145 vs ≠ 145 N Mean StDev SE Mean 95% CI T P 20 140.30 10.89 2.44 (135.20, 145.40) - 1.9 3 0.0 69 One-Sample Z: Calls (X1) Test of μ = 145 vs < 145 The assumed standard deviation = 10.89 N Mean S E Mea n 95% Upper Bound Z P 2 0 140. 30 2.4 4 144.31 - 1.9 3 0.0 27 D en Running Head: Course Project Part- B Appendix IV Descriptive Statistics: Time (X2) Variab le N N* Mean SE Mean StD ev Mini mum Q1 Medi an Q3 Time (X2) 100 0 15.338 0.230 2.3 00 10.0 00 13.6 00 15.0 50 17.2 25 Variable Maximum Time (X2) 20.000 Descriptive Statistics: Time (X2) Variab le N N* Mean SE Mean StD ev Mini mum Q1 Medi an Q3 Time (X2) 50 0 17.206 0.204 1.4 44 15.1 00 15.8 00 17.1 50 18.5 00 Variable Maximum Time (X2) 20.000 Running Head: Course Project Part- B One-Sample Z: Time (X2) Test of mu = 15 vs > 15 The assumed standard deviation = 1.444 95% Lower Variable N Mean StDev SE Mean Bound Z P Time (X2) 50 17.206 1.444 0.204 One-Sample Z: Time (X2) 16.870 10.80 0.0 00 Test of mu = 15 vs not = 15 The assumed standard deviation = 1.444