Collect 9.1 Coop. Asmnt. &…

9.10 ____________ bias and _______________ variability

9.2 Sample Proportions

Consider this… A polling organization asks a SRS of 1500 first-year college students whether they applied for admission to any other college. In fact, 35% of all first-year students applied to colleges besides the one they are attending. What is the probability that the random sample of 1500 students will give a result within 2 percentage points of this true value? What do you need to know in order to answer this question?

Sampling Distributions Activity Rice University Sampling Distribution Applet –Choose a couple of different sample sizes Note: the mean and standard deviation for the sampling distribution are algebraically derived from what we know about the mean and standard deviation of a binomial random variable.

P-hat = (Count of “successes” in sample)/(size of sample) = X/n

More formulas and their construction

“Rule of Thumb 2” gives exactly the same conditions for using a Normal approximation to the sampling distribution of p-hat as for a Normal approximation to the binomial. This should not be a surprise as proportions are just another way to look at counts.

Let’s work through Example 9.7 P 584

Step 1: Step 2: Step 3:

WORD CHOICE: “We see that almost 90% of all samples will give a result within 2 percentage points of the truth of the population” (p 585).

Ex 9.8 P 586

Step 1: Step 2: Step 3:

Fig 9.14

Another example Suppose a student taking a 100 question multiple choice final (with 5 possible answers each). This student didn’t study and must guess on every question. What is the probability that this student will get at least 30% right on the test?

How can we do this as a binomial? Context: 100 questions, 5 possible answers each, want to score at least 30%. P(X > 30) = = 1-binomcdf(100,.2,29) = How do the two computational methods compare?

Practice: 9.20 & 9.22 Homework: 9.25, 9.27, 9.30

Tomorrow: Q & A 9.2 Coop Asmnt