Session 2b Flashcards
Hypothesis Testing About a Single Mean - t-test purpose
Based on the sample mean (X) we test whether the population mean
(μ) is equal to some hypothesized value
Prior Requirements/Assumptions of t-test
The variable, X, in the population is normally distributed
The sample must be a simple random sample of the population (independence of observations)
A t-statistic is obtained by replacing the population standard deviation with the sample standard deviation, due to this replacement, the t-statistic does not follow the standard
normal distribution. Instead, it follows what
the t-distribution
The t distribution has what shape
Varies in shape according to the degrees of freedom, df = N − 1
The t distribution approaches a normal distribution as df (or sample size) becomes what
large
The distributions are quite close for df > 30.
The t distribution was discovered by William S. Gosset in 1908. Gosset was a statistician employed by the Guinness brewing company and he couldn’t publish under his own name. what is another name for the t distribution
students t distribution
Hypothesis Testing About Two Means - t-test
what is the purpose
To test whether two unknown population means (μ1 and μ2) are different from each other - based on their samples
for hypothesis testing aout 2 means (t-test), The two samples may be eitherwhat
independent or correlated
what are Independent samples also known as
Also known as “between-subjects” designs
Example: Each participant only goes through one of two conditions in an experiment
Mean preference scores for a brand between treatment (Ad) and control (No ad) groups of subjects
what is this an example of
independant samples
Correlated samples:
Also known as what
“dependent-subjects”, “paired-samples”, “repeated-measures”, and so on
Example: Each participant may go through both conditions in an experiment
Mean preference scores for a brand for before seeing an Ad and after seeing an Ad for the same subjects
what is this an example of
correlated samples
in independent sample t-tests, how are participants assigned
Participants are randomly assigned to one of two conditions:
Example: A marketing researcher wants to test the effect of a new ad on
consumers’ preference ratings
no ad – group one (control) – X1
ad – group 2 (treatment) – X2
Prior Requirements/Assumptions: for Independent Samples t-test
Both populations are normally distributed
The standard deviations (σ1 and σ2) of the populations are the same
– Homogeneity of variance (σ12 = σ2)
Each subject is independent
Simple random sample from population
