AP Statistics
Notes 10.2
After viewing the MythBusters video we are going to investigate whether the results of the experiment were really statistically significant by performing a simulation.
Let’s see what would happen just by chance if we randomly reassign the 50 people in this experiment to the two groups (yawn seed and no yawn seed) many times, assuming the treatment received doesn’t affect whether or not a person yawns.
In the MythBusters experiment, 14 people yawned and 36 didn’t. With that in mind, we will define Yawn as the numbers 1-14 and No Yawn as the numbers 15-50.
1. Use the randIntNoRep and STO> L1 to generate a random list of the numbers 1-50 with no repeats.
2. Of the 50 people in the sample, 34 people were in the Yawn Seed group. From the first 34 random numbers generated, record the number of people who yawned.
3. The other 16 people were in the No Yawn Seed group. From the remaining 16 random numbers generated, record the number of people who yawned.
4. Calculate the difference in the proportions who yawned for the two groups (yawn seed – no yawn seed).
Trial / Number who yawned in yawn seed group(34) / Number who yawned in No yawn seed group
(16) / Difference in proportions (yawn seed – no yawn seed)
1
2
3
4
5
5. Repeat Steps 1 to 4 four more times so that you have a total of 5 trials.
6. Make a class dotplot of the difference in proportions. In what percent of the class’s trials did the difference in proportions equal or exceed 0.0441 (what the MythBusters got in their experiment)?
7. Based on the class’s simulation results, how surprising would it be to get a result this large or larger simply due to the chance involved in the random assignment? Is the result statistically significant? Do not perform a significance test.
8. What conclusion would you draw about whether yawning is contagious? Explain.
Significance Test for p1 – p2
Hypothesis:Ho: p1-p2=0 OR Ho: p1=p2
Conditions:
· Random The data are produced by a random sample of size n1 from Population 1 and a random sample of size n2 from Population 2 or by two groups of size n1 and n2 in a randomized experiment.
· Normal n1p1≥10, n11-p1≥10 and n2p2≥10, n21-p2≥10
· Independent Both the samples or groups themselves and the individual observations in each sample or group are independent. When sampling without replacement, check that
10n1 ≤ population1 and 10n2 ≤ population2
2 Proportion z Test for p1 – p2:
z= p1-p2-0pC(1-pC)n1+pC(1-pC)n2
Example:
Are teenagers going deaf? In a study of 3000 randomly selected teenagers in 1988-1994, 15% showed some hearing loss. In a similar study of 1800 teenagers in 2005-2006, 19.5% showed some hearing loss. (These data are reported in Arizona Daily Star, August 18, 2010.) Do these data give convincing evidence that the proportion of all teens with hearing loss has increased? Between the two studies, Apple introduced the iPod. If the results of the test are statistically significant, can we blame iPods for the increased hearing loss in teenagers?