Ch 21: Confidence Intervals

a number that describes the population

1. a statistic (sample)

2. a parameter (population)

goal of statistical inference

draw conclusions about a population based on sample data

• what is the % of all employed men who have a college degree?

In a nationwide survey of n = 23,915 college seniors, 5,038 indicated plans to go to graduate or professional school. What is the sample statistic (p-hat)?

5,038/23,915 = 0.211 or 21.1%

margin of error

represents the range of values computed from our sample data by a process that is designed to capture the true population parameter in C% of all samples we could take

p (population parameter)

mean of the sampling distribution

standard error

standard deviation of our sampling distribution since we are doing all of this in the context of estimation

why do we use p-hat instead of just p?

b/c p-hate is an estimate while we don’t know the actual value of p

confidence intervals are frequentist in nature

based on the idea of lots of repeated sampling

the confidence interval (ex. 95%) is a probability

the probability that the method we are using produces an interval that captures the true population parameter in 95% of repeated samples

confidence intervals are approximate

this is because the sampling distribution of p-hate is only approximately normal. it is also because we are using the sample estimate p-hat rather than the true population value [ to compute our standard error

z* or critical value

z-scores with percentiles, for every degree of confidence there is a corresponding z* value

when do critical values apply?

only when using the normal distribution

increasing the confidence level does what to the interval?

makes it wider

greater confidence leads to ______ precision

less (b/c wider interval)

means sample statistic

x-bar

true population mean

mew

central limit theorem

as sample size increases, the sampling distribution of the statistics becomes more and more like the normal distribution

confidence level is a _______________ that says how often in many, many observations the method would produce an interval that does catch the true parameter value

probability

the standard deviation of the sampling distribution of the statistic is called the ____________ ________

standard error

true or false. we can do the process of confidence interval estimation for both means and proportions