Stat 1b kap 10

Question 1

Rules for Independent Random Samples

Answer 1

• 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.

Question 2

Confidence Interval for my1 − my2

Answer 2

1. 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.

2. Sampling distribution of xbar1-xbar2 is assumed to be normally distributed.

Question 3

If we know σ21 and σ22, then use the

Answer 3

z distribution

Question 4

If we do not know σ21 and σ22 but can assume that they are equal, then use the

Answer 4

t df distribution with a pooled estimate of the variance s2p.

Question 5

If we do not know σ21 and σ22 but cannot assume that they are equal, then use the

Answer 5

tdf distribution with s21 and s22.

Question 6

rules for matched-Pairs Sampling

Answer 6

• 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.

Question 7

Recognizing a Matched-Pairs Experiment

Answer 7

1. ” and “after” studies characterized by a measurement, some type of intervention, and another measurement, all on the same subject.
2. A pairing of observations, where it is not on the same subject that gets sampled twice

Question 8

Inference Concerning the Difference Between Two Proportions

Answer 8

1. 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
2. Pbar1-Pbar2 are defined for two independent random samples with n1 and n2 observations, respectively.

Question 9

Confidence Interval for p1 -p2

Answer 9

1. Since the population proportions p1 and p2 are unknown, we estimate them by pbar1 and pbar2 respectively, and
2. pbar1= x1/n1 and Pbar2=x2/n2 where x1 and x2 are the number of successes in n1 and n2 observations, respectively.

Question 10

The Test Statistic for Testing p1 − p2

Answer 10

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