Chapter 8: Estimating with Confidence

point estimator

a statistic that provides an estimate of a population parameter

point estimate

the value of a statistic from a sample

confidence interval

for a population parameter is an interval of plausible values for that parameter based on sample data. It is constructed in such a way that, with a chosen degree of confidence, the value of the parameter will be captured inside the interval.

confidence level C

The chosen degree of confidence. Confidence level gives an overall success rate of the method used to calculate the confidence interval.

Steps needed to write down to do a confidence interval problem

Step 1: Name the confidence Interval and define the parameter of interest

Step 2: Conditions (Random, Normality, 10% rule)

Step 3: Calculations

Step 4: Interpretations

Step 1 of confidence interval problems

(name of interval type) interval to estimate the proportion of (information in question)

Step 2: Conditions

Random: look for a part in question that says SRS or random and quote it then do a check next to it

Normality: np≥10 and n (1-p) ≥ 10 use p hat as a replacement since p is unknown

10% condition: make sure the population is greater than 10 times the sample size

Step 3: Calculations

The formula for any confidence interval point estimate + or - Margin of Error (look at formula in packet on page 9)

How do you calculate z*?

InvNorm, confidence level as area, tail in the center

Step 4: Interpretations (IMPORTANT Wording)

I am (level of confidence)____ confident that the true population of _______ is somewhere between ____ and _______.

What is the relationship between confidence level and population parameter?

If we were to select many random samples from a population and construct many C% confidence intervals using each sample, about C% of those intervals would capture the population parameter

What are t distributions?

They are used in statistics to estimate population parameters when the sample size is small or the population standard deviation is unknown. T distributions have a bell-shaped curve, similar to the normal distribution, but with heavier tails.

how is the dependence on the sample size calculated?

degrees of freedom (n-1)

rules about t*

• it is only used in confidence intervals estimating a population mean

• there are infinitely many t distributions

In Step 2 of Conditions what is different in a t* distribution compared to a z* problem?

Normality is calculated using Central Limit Theorem where sample size if greater than 30 is normal

If population is less than 30 how do we figure out if the distribution is normal?

Normal probability plots on our calculators will tell us if the probability is normal. To get full credit you need to graph this normal probability plot out roughly. Line trend means normal.

What is the t interval problem called

one sample t interval (for mean)

As the degrees of freedom increase the t distribution…

begins to look more normal