Ch 19 - Inference about a population proportion Flashcards
Assumptions for inference on proportions
If we call a given categorical characteristic in the population “success,” then the sample proportion of successes, (phat) is:
We treat a group of 120 Herpes patients with a new drug; 30 get better:p̂ =
The sampling distribution of p̂ and normality
is never exactly Normal. But for large enough sample sizes, it can be approximated by a Normal curve.
The mean and standard deviation (width)of the sampling distribution are both completely determined by
p and n.
Significance test for p
When p is unknown, both the __ and ___ are unknown
center and the spread of the sampling distribution
problem. We need to “guess” a value for p.
Large-sample confidence interval for p
use this method when the number of successes and the number of failures are both at least 15
Confidence intervals contain the population proportion p in C % of samples. For an SRS of size n drawn from a large population and with sample proportion p̂ calculated from the data, an approximate level C confidence interval for p is
Arthritis is a painful, chronic inflammation of the joints.
An experiment on the side effects of pain relievers examined arthritis patients to find the proportion of patients who suffer side effects.
Compute a 90% confidence interval for the population proportion of arthritis patients who suffer some “adverse symptoms.”
23 advers 440 total
Plus four” confidence interval for p
Use this method when C is at least 90% and sample size is at least 10.
We want a 90% CI for the population proportion of arthritis patients who suffer some “adverse symptoms.” using plue for method
23 advers 440 total
Sample size for a desired margin of error
What sample size would we need in order to achieve a margin of error no more than 0.01 (1 percentage point) with a 90% confidence level?
