10.3: Comparing Two Variances
F-Distribution
Properties of the F-Distribution
1. The F-distribution is a family of curves each of which is determined by two types of degrees of
freedom:
The degrees o
Chapter 6 Case Study:
_
Shoulder Heights of Appalachian Black Bears
Name:
Appalachian Bear Rescue (ABR) is a not-for-profit organization located near the Great Smokey
Mountains National Park. ABRs pro
6.4: Confidence Intervals for Variance and Standard Deviation
The Chi-Square Distribution
2
The point estimate for is
The point estimate for is
2
2
s is the most unbiased estimate for
You can use
7.1: Introduction to Hypothesis Testing
Hypothesis test
For example: An automobile manufacturer advertises that its new hybrid car has a
mean mileage of 50 miles per gallon. To test this claim, a samp
7.1B: Hypothesis Testing
Level of significance
Your maximum allowable probability of making a type I error.
By setting the level of significance at a small value, you are saying that you want the
pro
7.2B
Rejection Regions and Critical Values
Rejection region (or critical region)
Finding Critical Values in a Normal Distribution
1.
2.
3.
a. left-tailed,
b. right-tailed,
c. two-tailed,
4.
Example 1:
7.2: Hypothesis Testing for the Mean (Large Samples)
Decision Rule Based on P-value
To use a P-value to make a conclusion in a hypothesis test, compare the P-value with .
1.
2.
Example 1: The P-value
7.3: Hypothesis Testing for the Mean (Small Samples)
Finding Critical Values in a t-Distribution
1. Identify the level of significance, .
2. Identify the degrees of freedom d.f. = n 1.
3. Find the cri
7.4: Hypothesis Testing for Proportions
z-Test for a Population Proportion
A statistical test for a population proportion.
Can be used when a binomial distribution is given such that np 5 and nq 5.
7.5: Hypothesis Testing for Variance and Standard Deviation
2
Finding Critical Values for the -Test
1. Specify the level of significance, .
2. Determine the degrees of freedom d.f. = n 1.
3. The criti
8.1: Testing the Difference Between Means (Large Independent Samples)
Two Sample Hypothesis Test
Compares two parameters from two populations.
Sampling methods:
Independent Samples
Dependent Samples
8.2: Testing the Difference Between Means (Small Independent Samples)
Two Sample t-Test for the Difference Between Means
If samples of size less than 30 are taken from normally-distributed populations
8.3: Testing the Difference Between Means (Dependent Samples)
t-Test for the Difference Between Means
To perform a two-sample hypothesis test with dependent samples, the difference between
each data p
8.4: Testing the Difference Between Proportions
Two-Sample z-Test for Proportions
Used to test the difference between two population proportions, p and p .
1
2
Three conditions are required to conduct
9.1A: Correlations
Correlation
A relationship between two variables.
The data can be represented by ordered pairs ( x, y)
x is the
y is the
A scatter plot can be used to determine whether a linear
9.1B: Correlations Continued
Example 1: Finding the Correlation Coefficient
Calculate the correlation coefficient for the advertising expenditures and company sales
data. What can you conclude?
Advert
9.1C: Correlations & Causations
Hypothesis Testing for a Population Correlation Coefficient
A hypothesis test can also be used to determine whether the sample correlation
coefficient r provides enou
9.2: Linear Regression
Regression Lines
After verifying that the linear correlation between two variables is significant, next we
determine the equation of the line that best models the data (regress
9.3: Measures of Regression and Prediction Intervals
Variation About a Regression Line
Three types of variation about a regression line
To find the total variation, you must first calculate
The tota
10.1A: Goodness of Fit
Multinomial Experiment
Example: A radio station claims that the distribution of music preferences for listeners in the
broadcast region is as shown below.
Distribution
Classical
10.1B: Chi-Square Goodness-of-Fit Test
Chi-Square Goodness-of-Fit Test
For the chi-square goodness-of-fit test to be used, the following must be true.
1.
2.
If these conditions are satisfied, then the
10.2: Contingency Tables & Independence
r c contingency table
Shows the observed frequencies for two variables.
The observed frequencies are arranged in r rows and c columns.
The intersection of a
10.4: Analysis of Variance
One-way analysis of variance
Hypotheses:
H0: 1 = 2 = 3 = k (all population means are equal)
Ha: At least one of the means is different from the others.
In a one-way ANOVA t
6.1: Confidence Intervals for the Mean (Large Samples)
Point Estimate
Example 1: Market researchers use the number of sentences per advertisement as a measure
of readability for magazine advertisement
6.1 Homework
Name: _
1. Find the critical value that corresponds to a 94% confidence level.
For 2 - 5, Find the Margin of Error
2. Determine the sampling error if the grade point averages for 10 rando
6.2 Confidence Intervals for the Mean (Small Samples)
The t-Distribution
When the population standard deviation is unknown, the sample size is less than 30,
and the random variable x is approximately
6.3: Confidence Intervals for Population Proportions
Point Estimate for Population p
Population Proportion
Point Estimate for p
Point Estimate for q, the proportion of failures
Example 1: In a survey