Activity 7 Data

Section 1

Pop Secret Act II Proportions Test
Statistic
p-value 95% Conf Int Decision
Pop Total Pop Total P.S. Act II Pooled Diff lower upper
171 189 353 392 0.9048 0.9005 0.9019 0.0043 0.161 0.871773 -0.047025 0.055529 Retain
160 179 320 354 0.8939 0.9040 0.9006 -0.0101 -0.368 0.712868 -0.064674 0.044474 Retain
195 198 373 386 0.9848 0.9663 0.9726 0.0185 1.298 0.194149 -0.006239 0.043294 Retain
273 334 267 324 0.8174 0.8241 0.8207 -0.0067 -0.224 0.822549 -0.065325 0.051907 Retain
135 182 371 391 0.7418 0.9488 0.8831 -0.2071 -7.182 0.000000 -0.274321 -0.139860 Reject
178 199 341 407 0.8945 0.8378 0.8564 0.0566 1.867 0.061869 0.000917 0.112352 Retain
185 202 372 393 0.9158 0.9466 0.9361 -0.0307 -1.451 0.146676 -0.074997 0.013550 Retain
124 178 362 387 0.6966 0.9354 0.8602 -0.2388 -7.602 0.000000 -0.310609 -0.166933 Reject
133 195 351 386 0.6821 0.9093 0.8330 -0.2273 -6.937 0.000000 -0.298638 -0.155913 Reject
188 190 385 407 0.9895 0.9459 0.9598 0.0435 2.522 0.011669 0.017199 0.069856 Reject
172 196 352 383 0.8776 0.9191 0.9050 -0.0415 -1.612 0.106964 -0.094915 0.011897 Retain
146 181 353 363 0.8066 0.9725 0.9173 -0.1658 -6.616 0.000000 -0.225771 -0.105873 Reject
178 191 332 356 0.9319 0.9326 0.9324 -0.0006 -0.029 0.977081 -0.044853 0.043559 Retain
153 187 294 308 0.8182 0.9545 0.9030 -0.1364 -4.971 0.000001 -0.196339 -0.076388 Reject
183 196 360 389 0.9337 0.9254 0.9282 0.0082 0.364 0.716098 -0.035309 0.051756 Retain
192 198 374 402 0.9697 0.9303 0.9433 0.0393 1.960 0.049970 0.004862 0.073835 Reject
185 189 362 382 0.9788 0.9476 0.9580 0.0312 1.748 0.080476 0.000861 0.061523 Retain

Section 2

Pop Secret Act II Proportions Test
Statistic
p-value 95% Conf Int Decision
Pop Total Pop Total P.S. Act II Pooled Diff lower upper
189 201 324 378 0.9403 0.8571 0.8860 0.0832 2.997 0.002723 0.035018 0.131294 Reject
193 195 282 300 0.9897 0.9400 0.9596 0.0497 2.746 0.006026 0.019376 0.080111 Reject
166 192 382 393 0.8646 0.9720 0.9368 -0.1074 -5.012 0.000001 -0.158499 -0.056354 Reject
185 189 368 381 0.9788 0.9659 0.9702 0.0130 0.856 0.391927 -0.014490 0.040404 Retain
182 189 357 378 0.9630 0.9444 0.9506 0.0185 0.959 0.337356 -0.016952 0.053989 Retain
180 203 342 361 0.8867 0.9474 0.9255 -0.0607 -2.634 0.008434 -0.109981 -0.011357 Reject
166 185 344 371 0.8973 0.9272 0.9173 -0.0299 -1.207 0.227439 -0.081037 0.021184 Retain
138 175 355 388 0.7886 0.9149 0.8757 -0.1264 -4.206 0.000026 -0.192937 -0.059817 Reject
158 171 330 360 0.9240 0.9167 0.9190 0.0073 0.289 0.772954 -0.041610 0.056230 Retain
172 196 357 406 0.8776 0.8793 0.8787 -0.0018 -0.062 0.950591 -0.057528 0.054009 Retain
186 196 323 330 0.9490 0.9788 0.9677 -0.0298 -1.869 0.061609 -0.064314 0.004697 Retain
178 195 312 411 0.9128 0.7591 0.8086 0.1537 4.493 0.000007 0.096453 0.210939 Reject

Explanation

In this activity, each student popped two bags of microwave popcorn using the same microwave. Each row in the table represents the results of one student. One of the brands was Pop Secret and the second brand was Act II. Students flipped a coin and to determine which brand popcorn would be popped first.

A hypothesis test was then performed to see if there was a difference in the proportion of kernels that popped. The null hypothesis was H0: p1 = p2, where sample 1 was Pop Secret and sample 2 was Act II.

Summary Results

This table shows which brand had a higher pop rate.

Brand Statistical Tie Pop Secret Act II Total
Count 16 5 8 29
Percent 55.2% 17.2% 27.6% 100.0%