Chapter 7: Confidence Intervals Flashcards
What is a confidence interval?
Specifies range of values to estimate location of unknown pop parameter
What does the margin of error accompany?
Confidence level
What does the confidence level tell us?
How likely our parameter is to lie within that interval
What does the confidence level and margin of error together tell us?
How accurate our estimate is likely to be
What is a point estimate?
Single statistic used as best estimate or a alike parameter
What does accuracy refer to?
Freedom from error
What is freedom from error?
Estimate differs from parameter of interests value
What is the interval estimate?
Range of values parameter is likely to fall
What is the essence of sampling theory?
Probability sample will yield results that closely resemble those if we measured whole pop
What is a probability sample?
Every element known prob of being selected
What does the law of large numbers tell us?
With large sample, sample statistics approximate pop parameters very closely
What does a confidence level specify?
Probability that our particular sample will contain pop parameter
What happens with higher confidence levels?
lower the risk that interval estimate doesn’t have parameter
What happens with a lower confidence level?
Increases risk interval estimate doesn’t have parameter
What happens in the case of the 99% confidence interval?
99% of all samples drawn from the same population with same measure at same time will be ± amount of sampling error
What would a correct interpretation look like?
95% confident that our interval estimate of 150 to 165 pounds will in fact contain the true population value.
What do confidence interval statements actually mean?
we would expect to fail to capture the population mean in 5% of our samples (95)
What does a confidence interval specify?
Range of values that we estimate an unknown population parameter will fall
What does a confidence level specify?
Probability that population parameter will lie within that range
What happens with interval width and level of confidence?
Higher confidence level, wider confidence interval will be
What is the sampling error?
Whenever a sample rather than entire population is measured
What is the margin of error?
Estimate amount of difference that we think is possible between our statistic and corresponding parameter
What is the relationship between margin of error and sampling error?
How much sampling error we think is possible for given statistic
What is confidence interval effected by?
Amount of variation in pop, sample size
What happens with a greater sample size?
Smaller SD and smaller margin of error and sampling error
What is the central limit theorem?
With repeated samples sampling distribution will eventually become normal
What is a theoretical distribution?
Idea of conducting repeated samples infinitely
What are the two assumptions you need to calculate a confidence interval?
Used random sampling, normal distribution
What is the first scenario for calculating confidence interval?
Known pop sd
What are the elements of the first scenario for calculating confidence interval?
Use z and normal distribution to get critical value, use o to get standard error
What is the second scenario for calculating confidence interval?
Large sample and unknown pop sd
What are the elements of the second scenario of calculating confidence interval?
Use z and normal distribution to get critical value, use s to estimate o for standard error
What is the third scenario for calculating confidence interval?
Small sample and unknown pop sd
What are the elements for the third scenario of calculating confidence interval?
Use t and t-distribution to determine critical value, use s to estimate o for standard error
