Chapter 2: Hypothesis testing

Question 1

1. Parameter and statistic
2. Statistical Inference
3. Pop vs Sampling distribution
4. Sampling bias and variability

Answer 1

1. Parameter is charac of population, true value not known (u,sigma,N). Statistic is charac of a sample used to estimate the para. (x-bar,s,n)
2. Involves using info from the sample to draw conclusions regarding wider population.
3. Pop distri is the distri of values of variables among all individuals of the population. It is the distribution of values taken by statistic in all possible SAMPLES of same SIZE and from same POPULATN.
4. Bias: how close to CENTER (accuracy); Variability: how widely SPREAD (precision). Sampling bias can be eliminated by RANDOM sampling and to eliminate sampling variability chose larger population. But variability will not depend o saple size if population is 100 times greater than sample.

Question 2

1. Mean of sampling distribution of sample mean
2. SD of sampling distribution of sample mean
3. CENTRAL LIMIT THEOREM (CLT)

Answer 2

1. Sample means less variable and more normally distri than indi obs. Thus mean of sampling distribution is unbiased estimator of population mean. Ux-bar=u
2. SD of sampling distri SMALLER than population SD.
3. Sigma(x-bar)=sigma/under-root(n)
4. Larger sample size, sampling distribution of x-bar is closer to normal distribution irrespective of the population distribution as long as population has finite SD. SAMPLING DISTRIBUTION OF SAMPLE MEAN X-BAR is approx. Normal=> N(u,sigma/under-root n)

Question 3

How large sample size required for sampling distri of x-bar to be normal ?

Answer 3

More obs are req if population distribution is far from normal i.e. more skewed.

Question 4

Estimating with confidence

Answer 4

68-95-99.7 rule says that probability is about 0.95 that x-bar will be within 2 SD of mu. Then U is within 2 SD of x-bar.
95% OF ALL SAMPLES WILL CONTAIN TRUE U IN THE INTERVAL FROM X-2SD TO X+2SD

Question 5

CONFIDENCE INTERVALS

Answer 5

CI= ESTIMATE+ MARGIN OF ERROR;
Sigma(x-bar)=4.5 ; 95% of all samples will capture u in the interval x-bar+/-9

Question 6

CONFIDENCE LEVEL (C)

Answer 6

Overall capture rate if method used many times; probability of producing the interval that captures unk para
C:0-1