Confidence Intervals

Question 1

When we take a random sample we expect to get one of the most ______ or ______ values for the statistic.

Answer 1

Common or probable.

Question 2

If our random variable follows a _______ _______ then we can use _ _______ to….?

Answer 2

Normal Distribution

Z scores (Standard normal distribution)

identify the distance from the mean that would cover a certain % of values.

Need to know the population standard deviation to use this.

Question 3

Margin of error

Answer 3

shows how accurate we believe our statistic is, based on the

variability of the statistic

Our margin of error

Question 4

Explain 95% Confidence

Answer 4

When using a method to construct an interval for a sample mean, the mean for the chosen sample might fall out of bounds that enclose the central 95% of values in our distribution. The interval generated for our sample will not be valid as it doesn not contain the population mean.

We are only 95% confident this method of constructing intervals will work because we enclosed the central 95% of distribution.

Question 5

Confidence interval

Answer 5

an interval estimate of a population parameter.
Instead of relying on a single value to be our estimate of the parameter-that single value
would be the value of the statistic we compute-we instead provide a range or interval of
values that we believe the population parameter falls within

Question 6

How do you generate a confidence interval?

Answer 6

take a sample from a population, compute the sample statistic, and then
create an interval around that statistic that we believe the population parameter falls

Question 7

Confidence Interval is Constructed of two components

Answer 7

Point estimate (Sample statistic)

Margin of Error (E; a critical value and a measure of sampling error (standard deviation of the statistic))

Question 8

Critical Value

Answer 8

predetermined constant chosen based on desired level of confidence (e.g. Z value)

1. 96
2. 57

Question 9

estimate of sampling error

Answer 9

standard deviation of the sampling distribution of the statistic (e.g. 𝜎ൗ 𝑛 )