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: Population Standard Deviation (sigma): Sample size (n): Sample Mean (X-bar) 295 <-- Input the appropriate number for your situation 12 <-- Input the appropriate number for your situation 50 <-- Input the appropriate number for your situation 297.6 <-- Input the appropriate number for your situation Intermediate Calculations -Standard Error of the Estimate: 1.69705627 Test Statistic (z): 1.53206469 Results -- For the Alpha level given, H0 should be Alpha: 0.01 not rejected One tailed, H0: Mu =>295, p= 0.9372 One tailed, H0: Mu <=295, p= 0.0628 not rejected Two-tailed, H0: Mu = 295, p = 0.1255 not rejected timate), cel mpare it to ate number for your situation ate number for your situation ate number for your situation ate number for your situation pha level given, H0 should be 0.05 not rejected 0.1 not rejected not rejected Rejected not rejected not 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. Inputs -Hypothesized Population Mean: Sample Standard Deviation (s): Sample size (n): Sample Mean (X-bar) 7 <-- Input the appropriate number for your situation 1.05 <-- Input the appropriate number for your situation 60 <-- Input the appropriate number for your situation 7.25 <-- Input the appropriate number for your situation Intermediate Calculations -Standard Error of the Estimate: 0.135554 Test Statistic (t): 1.844278 Degrees of Freedom (d.f.): 59 Results -- For the Alpha level given, H0 should be Alpha: 0.01 0.05 not rejected not rejected One tailed, H0: Mu =>7, p= 0.9649 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 0 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 be 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: ate number for your situation ate number for your situation ate number for your situation he Alpha level given, H0 should be: 0.05 0.1 not rejected not rejected not rejected not rejected not rejected not rejected 17c9da1d5079f467a67006bd6bc26c3d17b94a40 Date Open High Low Close Adj Close Volume 12/31/2012 27.700001 28.41 27.700001 28.35 25.883875 5677700 1/2/2013 29.08 29.26 28.85 29.26 26.714716 7992800 1/3/2013 28.66 28.700001 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5/29/2015 6/1/2015 6/2/2015 6/3/2015 6/4/2015 6/5/2015 6/8/2015 6/9/2015 6/10/2015 6/11/2015 6/12/2015 6/15/2015 6/16/2015 6/17/2015 6/18/2015 6/19/2015 6/22/2015 6/23/2015 6/24/2015 6/25/2015 6/26/2015 6/29/2015 6/30/2015 7/1/2015 7/2/2015 7/6/2015 7/7/2015 7/8/2015 7/9/2015 40.759998 40.669998 40.68 41.02 41.610001 41.75 41.73 42.259998 42.32 41.790001 42 42.290001 42.490002 42.59 43.040001 42.84 42.200001 42.990002 43.169998 42.830002 42.880001 42.849998 42.639999 42.970001 42.98 42.849998 41.98 42.470001 42.68 43 43.110001 42.93 43.639999 44.049999 43.779999 43.369999 43.790001 44.459999 43.900002 43.720001 44.049999 44.529999 44.369999 44.290001 44.009998 43.049999 43.220001 43.709999 43.439999 42.869999 43.450001 42.57 43.060001 40.830002 41.209999 41.169998 41.889999 41.810001 41.84 42.450001 42.860001 42.48 41.919998 42.380001 42.799999 42.779999 43 43.150002 42.91 42.860001 43.669998 43.369999 43.110001 43.16 42.860001 43.09 43.099998 43.130001 42.919998 42.459999 43.099998 43 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11/16/2015 11/17/2015 11/18/2015 11/19/2015 11/20/2015 11/23/2015 11/24/2015 11/25/2015 11/27/2015 11/30/2015 12/1/2015 12/2/2015 12/3/2015 12/4/2015 12/7/2015 12/8/2015 37.5 38.400002 38.310001 37.369999 38.110001 38.259998 37.34 38.669998 39.110001 39.48 39.290001 39.830002 39.330002 39.310001 39.220001 38.880001 42 39.900002 40.18 40.759998 40.459999 41.259998 41.610001 41.009998 41.150002 42.419998 42.34 41.75 42.279999 42.77 42.580002 44.73 44.27 43.080002 44.110001 43.220001 42.529999 41.880001 43 43.169998 43.759998 43.75 43.5 43.189999 43.349998 43.41 43.52 43.740002 44.110001 43.52 42.93 44.099998 43.34 37.779999 38.720001 38.43 37.619999 38.27 38.68 38.290001 39.349998 39.560001 39.880001 39.950001 40.130001 39.66 39.650002 39.330002 39.52 42 40.700001 40.830002 40.959999 41.439999 41.77 41.779999 41.419998 42.880001 42.900002 42.43 42.709999 42.73 42.959999 43.68 45.240002 44.299999 43.84 44.119999 43.32 42.73 42.799999 43.490002 43.830002 43.849998 43.939999 43.91 43.560001 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