Stat 1b kap 10 Flashcards
Rules for Independent Random Samples
- Two (or more) random samples are considered independent if the process that generates one sample is completely separate from the process that generates the other sample.
- The samples are clearly delineated.
- 1 is the mean of the first population.2 is the mean of the second population.
Confidence Interval for my1 − my2
- xbar1-xbar2 is a point estimator for my1-my2
The values of the sample means and are computed from two independent random samples with n1 and n2 observations, respectively.
- Sampling distribution of xbar1-xbar2 is assumed to be normally distributed.
If we know σ21 and σ22, then use the
z distribution
If we do not know σ21 and σ22 but can assume that they are equal, then use the
t df distribution with a pooled estimate of the variance s2p.
If we do not know σ21 and σ22 but cannot assume that they are equal, then use the
tdf distribution with s21 and s22.
rules for matched-Pairs Sampling
- Parameter of interest is the mean difference D where D = X1 − X2 , and the random variables X1 and X2 are matched in a pair.
- Both X1 and X2 are normally distributed or n > 30.
Recognizing a Matched-Pairs Experiment
- ” and “after” studies characterized by a measurement, some type of intervention, and another measurement, all on the same subject.
- A pairing of observations, where it is not on the same subject that gets sampled twice
Inference Concerning the Difference Between Two Proportions
- Pbar1-Pbar2 (the difference between two sample proportions) is an unbiased point estimator of p1 − p2 (the difference between two population proportions).
is unbiased since 2. Pbar1-Pbar2 is unbiased since E(Pbar1-Pbar2)=p1-p2 - Pbar1-Pbar2 are defined for two independent random samples with n1 and n2 observations, respectively.
Confidence Interval for p1 -p2
- Since the population proportions p1 and p2 are unknown, we estimate them by pbar1 and pbar2 respectively, and
- pbar1= x1/n1 and Pbar2=x2/n2 where x1 and x2 are the number of successes in n1 and n2 observations, respectively.
The Test Statistic for Testing p1 − p2
The test statistic is assumed to follow the z distribution.
If the hypothesized difference d0 is not zero, then the value of the test statistic is