Activity 8 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
411 457 364 381 0.8993 0.9554 0.9248 -0.0560 -3.063 0.002189 -0.090544 -0.021530 Reject
430 495 336 365 0.8687 0.9205 0.8907 -0.0519 -2.409 0.015990 -0.092543 -0.011179 Reject
456 503 382 456 0.9066 0.8377 0.8738 0.0688 3.206 0.001344 0.026507 0.111175 Reject
405 460 350 363 0.8804 0.9642 0.9174 -0.0838 -4.333 0.000015 -0.119030 -0.048475 Reject
395 462 282 355 0.8550 0.7944 0.8286 0.0606 2.279 0.022666 0.007711 0.113514 Reject
392 481 321 389 0.8150 0.8252 0.8195 -0.0102 -0.390 0.696624 -0.061496 0.041048 Retain
410 431 347 365 0.9513 0.9507 0.9510 0.0006 0.039 0.969288 -0.029518 0.030700 Retain
372 428 347 374 0.8692 0.9278 0.8965 -0.0586 -2.720 0.006524 -0.099985 -0.017313 Reject
426 499 354 389 0.8537 0.9100 0.8784 -0.0563 -2.548 0.010848 -0.098390 -0.014247 Reject
362 504 254 362 0.7183 0.7017 0.7113 0.0166 0.532 0.595003 -0.044753 0.077947 Retain
347 513 356 374 0.6764 0.9519 0.7926 -0.2755 -9.991 0.000000 -0.321388 -0.229528 Reject
438 471 363 377 0.9299 0.9629 0.9446 -0.0329 -2.082 0.037297 -0.062857 -0.003000 Reject
343 480 308 378 0.7146 0.8148 0.7587 -0.1002 -3.407 0.000657 -0.156496 -0.043967 Reject
360 467 352 381 0.7709 0.9239 0.8396 -0.1530 -6.040 0.000000 -0.199503 -0.106510 Reject
444 459 355 375 0.9673 0.9467 0.9580 0.0207 1.480 0.138936 -0.007307 0.048614 Retain
407 429 339 346 0.9487 0.9798 0.9626 -0.0311 -2.264 0.023559 -0.056658 -0.005444 Reject
441 509 357 393 0.8664 0.9084 0.8847 -0.0420 -1.958 0.050232 -0.083064 -0.000920 Retain
392 494 315 370 0.7935 0.8514 0.8183 -0.0578 -2.181 0.029164 -0.108701 -0.006957 Reject
363 487 256 281 0.7454 0.9110 0.8060 -0.1657 -5.592 0.000000 -0.216692 -0.114612 Reject
470 528 435 446 0.8902 0.9753 0.9292 -0.0852 -5.163 0.000000 -0.115493 -0.054876 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
454 519 331 376 0.8748 0.8803 0.8771 -0.0056 -0.250 0.802546 -0.049003 0.037883 Retain
342 480 347 381 0.7125 0.9108 0.8002 -0.1983 -7.227 0.000000 -0.247848 -0.148675 Reject
403 450 351 372 0.8956 0.9435 0.9173 -0.0480 -2.486 0.012909 -0.084715 -0.011271 Reject
297 489 293 365 0.6074 0.8027 0.6909 -0.1954 -6.112 0.000000 -0.254875 -0.135880 Reject
470 491 543 579 0.9572 0.9378 0.9467 0.0194 1.409 0.158968 -0.007186 0.045999 Retain
356 434 307 342 0.8203 0.8977 0.8544 -0.0774 -3.034 0.002412 -0.125724 -0.029044 Reject
454 508 374 392 0.8937 0.9541 0.9200 -0.0604 -3.311 0.000931 -0.094259 -0.026503 Reject
347 490 317 358 0.7082 0.8855 0.7830 -0.1773 -6.187 0.000000 -0.229354 -0.125270 Reject
342 429 361 371 0.7972 0.9730 0.8788 -0.1758 -7.598 0.000000 -0.217307 -0.134379 Reject
336 433 366 378 0.7760 0.9683 0.8656 -0.1923 -8.008 0.000000 -0.235337 -0.149207 Reject
417 511 382 409 0.8160 0.9340 0.8685 -0.1179 -5.260 0.000000 -0.159261 -0.076615 Reject
347 389 378 412 0.8920 0.9175 0.9051 -0.0254 -1.228 0.219377 -0.066152 0.015262 Retain
342 480 428 464 0.7125 0.9224 0.8157 -0.2099 -8.315 0.000000 -0.257156 -0.162671 Reject
244 369 334 364 0.6612 0.9176 0.7885 -0.2563 -8.498 0.000000 -0.312283 -0.200389 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 8 2 24 34
Percent 23.5% 5.9% 70.6% 100.0%