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
157 167 420 443 0.9401 0.9481 0.9459 -0.0080 -0.388 0.698318 -0.049456 0.033533 Retain
189 206 413 434 0.9175 0.9516 0.9406 -0.0341 -1.707 0.087769 -0.076792 0.008518 Retain
163 167 425 439 0.9760 0.9681 0.9703 0.0079 0.514 0.607020 -0.020485 0.036363 Retain
146 161 413 436 0.9068 0.9472 0.9363 -0.0404 -1.795 0.072635 -0.089975 0.009144 Retain
148 189 352 378 0.7831 0.9312 0.8818 -0.1481 -5.152 0.000000 -0.212208 -0.084089 Reject
158 194 379 452 0.8144 0.8385 0.8313 -0.0241 -0.749 0.454121 -0.088433 0.040308 Retain
186 193 416 438 0.9637 0.9498 0.9540 0.0140 0.772 0.440360 -0.019420 0.047337 Retain
164 181 373 441 0.9061 0.8458 0.8633 0.0603 1.988 0.046832 0.006030 0.114514 Reject
176 184 423 437 0.9565 0.9680 0.9646 -0.0114 -0.704 0.481244 -0.045218 0.022335 Retain
165 184 442 470 0.8967 0.9404 0.9281 -0.0437 -1.945 0.051759 -0.092586 0.005213 Retain
163 184 414 431 0.8859 0.9606 0.9382 -0.0747 -3.523 0.000427 -0.124170 -0.025205 Reject
153 182 350 378 0.8407 0.9259 0.8982 -0.0853 -3.126 0.001774 -0.144633 -0.025901 Reject
175 183 385 449 0.9563 0.8575 0.8861 0.0988 3.547 0.000390 0.054969 0.142678 Reject
187 193 362 384 0.9689 0.9427 0.9515 0.0262 1.382 0.166953 -0.007558 0.059965 Retain
188 192 419 439 0.9792 0.9544 0.9620 0.0247 1.494 0.135195 -0.003358 0.052807 Retain
162 183 363 398 0.8852 0.9121 0.9036 -0.0268 -1.017 0.309010 -0.080727 0.027098 Retain
151 184 373 462 0.8207 0.8074 0.8111 0.0133 0.390 0.696832 -0.052783 0.079369 Retain
190 196 430 453 0.9694 0.9492 0.9553 0.0202 1.141 0.253741 -0.011309 0.051629 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
184 188 397 427 0.9787 0.9297 0.9447 0.0490 2.449 0.014338 0.017151 0.080811 Reject
176 184 383 449 0.9565 0.8530 0.8831 0.1035 3.681 0.000233 0.059458 0.147572 Reject
163 191 362 450 0.8534 0.8044 0.8190 0.0490 1.473 0.140870 -0.013163 0.111080 Retain
162 171 426 460 0.9474 0.9261 0.9319 0.0213 0.943 0.345727 -0.019849 0.062412 Retain
174 178 383 429 0.9775 0.8928 0.9176 0.0848 3.458 0.000545 0.048268 0.121241 Reject
176 181 394 445 0.9724 0.8854 0.9105 0.0870 3.457 0.000546 0.048956 0.125009 Reject
137 184 374 428 0.7446 0.8738 0.8350 -0.1293 -3.950 0.000078 -0.199695 -0.058838 Reject
124 130 438 462 0.9538 0.9481 0.9493 0.0058 0.266 0.790175 -0.035563 0.047151 Retain
142 145 251 265 0.9793 0.9472 0.9585 0.0321 1.561 0.118585 -0.003386 0.067667 Retain
163 166 405 416 0.9819 0.9736 0.9759 0.0084 0.595 0.551813 -0.017093 0.033833 Retain
141 193 355 455 0.7306 0.7802 0.7654 -0.0496 -1.364 0.172555 -0.122900 0.023600 Retain
159 177 342 457 0.8983 0.7484 0.7902 0.1499 4.160 0.000032 0.090233 0.209659 Reject
164 192 380 426 0.8542 0.8920 0.8803 -0.0379 -1.341 0.179825 -0.095825 0.020121 Retain
144 185 333 422 0.7784 0.7891 0.7858 -0.0107 -0.296 0.766941 -0.082114 0.060672 Retain
180 199 367 419 0.9045 0.8759 0.8851 0.0286 1.043 0.297053 -0.022984 0.080239 Retain
173 189 361 451 0.9153 0.8004 0.8344 0.1149 3.567 0.000361 0.060720 0.169081 Reject
161 173 397 428 0.9306 0.9276 0.9285 0.0031 0.132 0.894962 -0.042061 0.048192 Retain
175 192 372 434 0.9115 0.8571 0.8738 0.0543 1.887 0.059144 0.002369 0.106262 Retain
157 205 255 317 0.7659 0.8044 0.7893 -0.0386 -1.055 0.291412 -0.111136 0.034010 Retain

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 25 8 4 37
Percent 67.6% 21.6% 10.8% 100.0%