Discuss the process to perform hypothesis testing problems about a population proportion using the z statistic.

Hypothesis testing is a way of using data to draw conclusions about the population. When performing hypothesis tests concerning population proportions, the z-statistic should be used. The process for performing a hypothesis test on a population proportion involves five steps: formulating hypotheses, defining level of significance, calculating the value of the test statistic, comparing the test statistic to critical values, and drawing conclusions.

The first step in this process is to formulate null and alternative hypotheses (Ho and Ha). The null hypothesis states that there is no difference between what you would expect if there were no real effect – i.e., Ho: P=p0 where p0 represents your expected parameter value in Ho. The alternative hypothesis states that there is an effect – i.e., Ha: P≠p0 or p>p0 or p
The second step is to define the level of significance as α which determines how likely it will be for us to reject Hₒ after we have calculated our z-statistic from sample data accordingly. Generally speaking, any α less than 0.05 will be accepted as significant since this means that our results will only happen by chance 5% of the time or less when Ho was true all along; if α > 0.05 then we cannot reject Hₒ and must accept Ho as true instead because our results were too likely due to randomness alone so they do not provide enough evidence against Ho being correct in such cases2 .

Discuss the process to perform hypothesis testing problems about a population proportion using the z statistic.

The third step is to calculate the value of our z-statistic based on sample data provided while also taking into account parameters such as standard deviation and degrees freedom accordingly3 . This allows us determine how far away our calculated mean falls away from what we would expect given some established assumptions according our initial formulation in Step 1 (i.e., using p0). From here onwards it becomes possible for us identify whether these differences could reasonably happened due randomness alone4 .

Fourthly we compare this test statistic’s numerical result with its corresponding critical values at either side of it based on their respective confidence intervals5 . If both sides are greater than their respective critical values then this means that it was too unlikely for them occur randomly thus providing sufficient evidence against accepting Hₒ6 ; similarly but oppositely if both sides are lesser than their respective critical values then it was too likely for them occur randomly thus providing insufficient evidence against accepting Hₒ7 instead 8 . Therefore any scenario where one side or none both pass/fail provides an indication towards rejecting/accepting Hₒ respectively9 10 respectively11 .

As an example I can use this process within my role as a property manager when trying to determine whether leasing fees charged by competitors affects my occupancy rate at certain rental properties I manage12 ,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 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 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269

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