STA2014 - CH 9
point estimate
A point estimate is the value of a statistic that estimates the value of a parameter.
The procedure for constructing a confidence interval about a mean is _______, which means minor departures from normality do not affect the accuracy of the interval.
robust Note that a confidence interval about μ can be computed for non-normal populations even though Student's t-distribution requires a normal population. This is because the procedure for constructing the confidence interval is robust—it is accurate despite minor departures from normality. Sample data should always be inspected for serious departures from normality and for outliers.
The requirements for constructing a confidence interval about p are that the sample is a simple random sample,
the value of np^(1-p^) is greater than or equal to 10, and the sample size is less than or equal to 5% of the population size.
How does decreasing the sample size affect the margin of error, E?
As the sample size decreases, the margin of error increases.
What does "95% confidence" mean in a 95% confidence interval?
If 100 different confidence intervals are constructed, each based on a different sample of size n from the same population, then we expect 95 of the intervals to include the parameter and 5 to not include the parameter.
Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.14. Each independently constructed a confidence interval based on the point estimate, but Jaime's interval has a lower bound of 0.137 and an upper bound of 0.143, while Mariya's interval has a lower bound of 0.116 and an upper bound of 0.191. Which interval is wrong? Why?
Mariya's interval is wrong because it is not centered on the point estimate.
What type of variable is required to construct a confidence interval for a population proportion?
Qualitative with 2 possible outcomes
Suppose you have two populations: Population A—All students at a state college (N=21,000) and Population B—All residents of a town in the state (N=21,000). You want to estimate the mean age of each population using two separate samples each of size n=75. If you construct a 95% confidence interval for each population mean, will the margin of error for population A be larger, the same, or smaller than the margin of error for population B? Justify your reasoning.
The margin of error for Population A will be smaller because its sample standard deviation will be smaller.
What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?
The researcher could decrease the level of confidence.
A government's congress has 895 members, of which 131 are women. An alien lands near the congress building and treats the members of congress as as a random sample of the human race. He reports to his superiors that a 95% confidence interval for the proportion of the human race that is female has a lower bound of 0.123 and an upper bound of 0.169. What is wrong with the alien's approach to estimating the proportion of the human race that is female?
The sample is not a simple random sample.
level of confidence, represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted left parenthesis 1 minus alpha right parenthesis times 100 %.
The level of confidence represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted (1-α) • 100%.
confidence interval
To construct a confidence interval for the mean, the distribution of the mean must be normal. For the distribution of the mean to be normal, the data must come from a normal population or the sample must be large.
smaller margin of error
larger sample size more than compensates for the higher level of confidence
