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 Mall of Elbonia Interview Results Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Gender 1 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 1 Clothing $65 $139 $186 $125 $193 $186 $60 $231 $83 $157 $185 $125 $174 $125 $110 $164 $192 $165 $123 $189 $115 $116 $188 $146 $184 $121 $169 $95 $135 $157 $163 $134 $179 $144 $180 $92 $154 $180 $168 $117 $193 $96 $118 $214 $169 $113 Food $16 $17 $22 $24 $17 $20 $18 $18 $20 $20 $26 $18 $17 $26 $18 $18 $15 $28 $18 $19 $16 $27 $13 $24 $24 $19 $15 $16 $24 $26 $12 $19 $24 $21 $20 $15 $19 $26 $13 $25 $17 $24 $13 $28 $18 $16 Time in Mall Friendliness 51 8 40 5 231 3 131 5 20 3 204 2 61 4 64 1 84 5 161 5 148 7 67 10 231 6 165 1 59 9 16 2 174 3 41 7 337 5 63 9 57 8 242 7 12 8 116 9 46 9 146 7 152 4 61 1 71 1 226 9 48 7 289 10 81 6 170 3 53 10 161 9 34 7 111 5 53 6 125 1 101 10 130 9 108 4 109 6 141 2 185 7 Attractiveness 9 8 1 8 3 1 3 5 7 5 6 9 4 5 5 3 1 1 4 10 9 8 6 7 7 8 4 1 9 10 10 9 5 5 5 9 8 7 5 1 8 8 1 9 1 9 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 $199 $64 $177 $149 $130 $186 $180 $93 $114 $195 $185 $81 $223 $164 $119 $165 $146 $87 $158 $187 $113 $159 $174 $169 $140 $126 $177 $124 $181 $124 $145 $186 $118 $141 $154 $161 $92 $183 $215 $104 $178 $155 $104 $171 $172 $88 $208 $98 $26 $13 $23 $24 $15 $24 $17 $24 $15 $20 $21 $15 $29 $16 $17 $20 $19 $24 $20 $26 $12 $27 $18 $21 $17 $23 $18 $21 $17 $26 $13 $21 $24 $19 $16 $20 $26 $20 $15 $19 $21 $18 $19 $26 $17 $19 $22 $19 95 136 45 102 81 205 26 237 229 39 125 318 64 124 127 89 98 145 124 118 161 42 39 210 242 170 76 149 161 24 77 239 87 20 90 52 97 42 222 167 36 87 213 74 235 56 67 215 10 5 8 6 9 5 1 1 9 9 5 5 1 2 8 7 3 6 8 7 8 3 2 6 2 1 9 8 7 7 6 3 9 2 1 5 2 10 8 2 8 8 6 10 8 1 9 1 9 2 4 5 7 8 4 3 8 10 3 9 3 3 7 8 7 8 10 6 2 1 2 1 6 9 8 9 7 8 8 1 4 2 9 4 7 8 9 1 7 7 7 8 1 3 9 1 95 96 97 98 99 100 0 0 0 1 0 0 $174 $149 $140 $170 $177 $79 $21 $22 $23 $13 $27 $17 46 333 39 39 57 235 1 10 5 4 1 6 1 7 1 5 3 8