What is the status of for z-based confidence intervals for a population mean?
is known
What is the status of for t-based confidence intervals for population mean?
is unknown
What two things does Statistical Inference involve?
Estimation
Hypothesis
What do we use statistical inferences for?
To make inferences about a parameter
What are the two types of estimates of parameters?
Point estimate
Interval estimate
What is a Interval Estimate?
It's a point estimate with a +/- Margin of Error
What is the purpose of an Interval Estimate?
Provide info about how close the point estimate is to the parameter
In an Interval Estimate, what does the Width depend on?
How much confidence you want in your estimate
What is Precision?
Width of an interval
What is Accuracy?
Probability of the estimate being correct, defined as
What is the general form of the interval estimate for the population mean?
+/- Margin of Error
What is the interval estimate of equation if is known?
What is ?
The confidence coefficient
What is ?
The z-value that provides an area of in the upper tail of the standard normal prob distribution
Assume:
Population of all individual car mileages is ND
Standard deviation () is 0.8
A sample size (n) of 50
Build a 95% interval estimate of
We have 95% confidence that will be within +/- .22 mpg of the population mean
(from z-table)
Margin of error = (1.96)(.113) = .22
If we have 95% confidence that will be within +/- .22 mpg of the population mean...
Assume = 31.56
What is the confidence interval?
[31.56 +/- 0.22] = [31.34, 31.78]
If = 0.10 (90% confidence) what is the confidence interval width?
1.645
If = 0.05 (95% confidence) what is the confidence interval width?
1.96
If = 0.01 (99% confidence) what is the confidence interval width?
2.576
What probability of values is between z-scores of -1.645 and +1.645?
0.9000
What probability of values is between z-scores of -1.96 and +1.96?
0.9500
What probability of values is between z-scores of -2.576 and +2.576?
0.9900
What is used instead of when it is not known?
s
Sample standard deviation
What is the t-score standard error equation?
What is the t-score equation?
What are the differences between the t-distribution and the z-distribution?
t-distribution is more spread out than the standard normal (z-distribution)
t-distribution is defined by the # of degrees of freedom (df = n - 1)
What happens to the degrees of freedom (df) as n (sample size) increases?
df increases
What happens to the t-curve as the degrees of freedom (df) increases?
t-curve narrows
Spread decreases
Eventually approaches the standard normal curve
At what sample size does the t-curve become very similar to the z-curve?
At what sample size is the z-distribution used INSTEAD of the t-distribution?
What's the differences between the t-table and the z-table?
t-table shows values to the RIGHT of the t-score
t-table is based on df and not n
What is the Confidence Interval equation for the t-distribution ( is not known)?
In a sample of 16 management consultants, the following statistics about hourly wages have been computed:
Construct a 95% confidence interval (C.I.) estimate.