Exam 1 Flashcards
A statement that specifies some testable relationship among variables
Hypothesis
A statement of no difference, no effect, no relationship, or independence among the variables
Null Hypothesis
A statement in which a difference effect, relationship, or dependence is expected
Alternative Hypothesis
H0: μ = μ0
H1: μ ≠ μ0
Two-tailed test
H0: μ ≤ μ0
H1: μ > μ0
Right-tailed test
H0: μ ≥ μ0
H1: μ < μ0
Left-tailed test
Hypothesis are always stated in _______, NOT ______.
Always population parameters, NEVER sample statistics
Identifying null and alternative hypotheses (3):
- Identify the specific claim or hypothesis to be tested and put it into symbolic form
- Give the symbolic form of the claim that must be true when the original claim is false
- Of the two symbolic expressions obtained so far, let the null hypothesis (H0) be the one that contains some form of equality ( =, less than or equal to, greater than or equal to). The other symbolic expression becomes the alternative hypothesis (H1)
Hypothesis Example:
Claim: The population of U.S. commercial aircraft has an average age of 10 years or less
What is the null and alternative hypothesis?
- μ ≤ 10
- μ > 10
- H0: μ ≤ 10
H1: μ > 10
Hypothesis Example:
Company XYZ will introduce a new product nationally if test market results indicate more than a 20% market share
H0: π ≤ .20
Ha: π > .20
Hypothesis Example:
Michigan State claims that the average GMAT score for entering MBAs is 640.
H0: μ = 640
Ha: μ ≠ 640
Hypothesis Example:
The average weight of the offensive linemen on MSU’s football team is less than 325 pounds.
H0: μ ≥ 325
Ha: μ < 325
Where is the rejection region?
Calculated value > table value
Or
-Calculate value < -table value
Hypothesis Testing Procedure (5):
- Specify the null and alternative hypotheses
- Choose the appropriate statistical test
- Specify the desired level of significance, i.e. the alpha level
- Compute the value of the test statistic
- Compare the table value from step 3 to the calculated value from step 4
Rejecting a true null hypothesis
Type I Error
Accepting a false null hypothesis
Type II Error
Nominal examples and measures of central tendencies and dispersion:
Examples:
- Male-female
- User-nonuser
- Occupations
- Uniform numbers
Measure of central tendency: mode
Measure of dispersion: frequencies
Ordinal examples and measures of central tendencies and dispersion:
Examples:
- Brand preference
- Movie Ratings
- Grades of Lumber
Measure of central tendency: Median
Measure of dispersion: Inter-quartile range
Interval examples and measures of central tendencies and dispersion:
Examples:
- Temperature scale
- GPA
Measure of central tendency: Mean
Measure of dispersion: Standard Deviation
Ratio examples and measures of central tendencies and dispersion:
Examples:
- Number of units sold
- Number of purchasers
- Weight
Measure of central tendency: Mean
Measure of dispersion: Standard Deviation
Basic points concerning measurement scales (3):
- The higher order scale possesses all of the information that a lower order scale possesses
- The highest type of scale you can use is determined by the attribute you are measuring
- If you use a statistic that is inappropriate for the type of date that you have, the results will be meaningless
Measurements:
Lowest =
Highest =
Lowest = Nominal Highest = Ratio
Assumptions of the T-test (4):
- The variable is normally distributed in both populations
- The population variances are unknown but assumed to be equal
- The samples are independent
- The sample sizes are less than 30 for either sample
What is n1 and n2?
What is x1 and x2?
What is D0?
What is Sp^2?
n1 & n2: sample sizes
x1 and x2: sample means
D0: Hypothesized difference in population means
Sp^2: Pooled estimate of the variance
What is S1^2 and S2^2?
The sample variances
How do you find the degrees of freedom?
n1 + n2 - 2
If the degrees of freedom do not match a number in the table, always use the _____.
lower df value
Unless otherwise specified, a =
.05
