chapter 12: other one-sample test statistics

Question 1

example for when a researcher wants to test a hypothesis about a population proportion

Answer 1

an opinion pollster wants to know whether the majority of voters favor a certain candidate

Question 2

assumptions used when testing a population proportion

Answer 2

1. random sampling from population of interest
2. binomial population
3. np0 and n(1-p0) are both greater than 15
4. population is at least 10x larger than the sample
   - Ho is rejected if the z statistic falls in the critical region

Question 3

use the z statistic for testing Ho about a population proportion with the equation…

Answer 3

z=pˆ−p0/ √p0 (1−p0)/n

pˆ is the sample estimator of the population and is given by

pˆ= # of successes in the random sample / # of observations in the random sample

Po is the value of the population proportion specified in the Ho

n is the size of the random sample used to compute pˆ

Question 4

what are the 3 things to specify when choosing a sample size

Answer 4

1. m* acceptable margin of error in estimating p
   - how close you want the sample proportion to be to the population proportion
   - typically between the .02 and .04
2. select a confidence level and associated z values from table D.2 *typically the 95% CI is used
3. make an educated guess about the likely values of p, denoted p*