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
180 190 377 398 0.9474 0.9472 0.9473 0.0001 0.007 0.994646 -0.038475 0.038739 Retain
187 189 388 414 0.9894 0.9372 0.9536 0.0522 2.827 0.004700 0.024671 0.079769 Reject
189 191 372 388 0.9895 0.9588 0.9689 0.0308 2.006 0.044909 0.006274 0.055257 Reject
184 196 381 412 0.9388 0.9248 0.9293 0.0140 0.630 0.528578 -0.028116 0.056152 Retain
183 193 394 421 0.9482 0.9359 0.9397 0.0123 0.596 0.551484 -0.026738 0.051377 Retain
171 185 386 404 0.9243 0.9554 0.9457 -0.0311 -1.547 0.121951 -0.074217 0.011974 Retain
174 179 403 428 0.9721 0.9416 0.9506 0.0305 1.580 0.114168 -0.002330 0.063286 Retain
122 156 211 284 0.7821 0.7430 0.7568 0.0391 0.914 0.360504 -0.043249 0.121436 Retain
127 150 306 372 0.8467 0.8226 0.8295 0.0241 0.662 0.507854 -0.045425 0.093597 Retain
206 208 353 376 0.9904 0.9388 0.9572 0.0516 2.947 0.003206 0.023940 0.079170 Reject
210 217 346 379 0.9677 0.9129 0.9329 0.0548 2.573 0.010073 0.017958 0.091669 Reject
112 129 298 316 0.8682 0.9430 0.9213 -0.0748 -2.660 0.007809 -0.138541 -0.011101 Reject
294 296 365 399 0.9932 0.9148 0.9482 0.0785 4.615 0.000004 0.049515 0.107397 Reject

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
180 180 422 426 1.0000 0.9906 0.9934 0.0094 1.304 0.192109 0.000231 0.018548 Retain
182 187 387 420 0.9733 0.9214 0.9374 0.0518 2.434 0.014937 0.017239 0.086428 Reject
174 177 407 419 0.9831 0.9714 0.9748 0.0117 0.833 0.405094 -0.013142 0.036523 Retain
167 169 400 427 0.9882 0.9368 0.9513 0.0514 2.629 0.008573 0.023136 0.079659 Reject
169 197 357 415 0.8579 0.8602 0.8595 -0.0024 -0.079 0.937098 -0.061453 0.056707 Retain
182 194 385 402 0.9381 0.9577 0.9513 -0.0196 -1.040 0.298184 -0.058760 0.019626 Retain
161 194 413 423 0.8299 0.9764 0.9303 -0.1465 -6.634 0.000000 -0.201280 -0.091645 Reject
181 189 347 416 0.9577 0.8341 0.8727 0.1235 4.226 0.000024 0.077695 0.169380 Reject
168 196 404 426 0.8571 0.9484 0.9196 -0.0912 -3.887 0.000102 -0.144520 -0.037908 Reject
53 92 320 394 0.5761 0.8122 0.7675 -0.2361 -4.827 0.000001 -0.344190 -0.128002 Reject
166 187 311 397 0.8877 0.7834 0.8168 0.1043 3.041 0.002361 0.043581 0.165070 Reject
151 174 331 411 0.8678 0.8054 0.8239 0.0625 1.813 0.069794 -0.000764 0.125691 Retain
175 188 347 382 0.9309 0.9084 0.9158 0.0225 0.908 0.363670 -0.023918 0.068866 Retain
197 229 352 374 0.8603 0.9412 0.9104 -0.0809 -3.377 0.000732 -0.131759 -0.030070 Reject
190 197 370 408 0.9645 0.9069 0.9256 0.0576 2.530 0.011392 0.019348 0.095860 Reject
181 196 348 404 0.9235 0.8614 0.8817 0.0621 2.208 0.027240 0.011879 0.112288 Reject
227 236 378 426 0.9619 0.8873 0.9139 0.0745 3.275 0.001058 0.035828 0.113253 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 13 12 5 30
Percent 43.3% 40.0% 16.7% 100.0%