psyc 243 test 2
the two requirements for a random sample are
(1) each individual has an equal chance of being selected, and (2) if more than one individual is selected, the probabilities must stay constant for each individual selected.
(a)A psychology class consists of 32 freshmen and 48 sophomores. If the professor selects names from the class list using random sampling. What is the probability that the first student selected will be a freshman?
0.40
(a)If a random sample of n = 6 students is selected and the first five selected are sophomores, what is the probability that the sixth student selected will be a freshman?
0.40
Four assumptions should be true (or close to true)when using the t-statistic:
1. The data are continuous. 2. The sample data have been randomly sampled from the population. 3. The variability of the data in each group is similar. For Independent-Measures t-Tests this means the variances of the populations that samples are drawn from are similar. 4. The sampled population is approximately normally distributed.
The four steps of a hypothesis test are:
1.State the hypotheses and select an alpha level. 2.Locate the critical region. 3.Compute the test statistic. 4.Make a decision to reject or fail to reject the null hypothesis.
(a)What is the probability that the first student selected will be a freshman after 10 sophomores students join the class?
32/90 (.36)
Does a hypothesis test allow a researcher to claim that an alternative hypothesis is true?
A hypothesis test does not allow a researcher to claim that an alternative hypothesis is true. A hypothesis test compares the probability of obtaining the sample data if the null hypothesis were true to α, which is the criterion for rejecting the null hypothesis.
Two-tailed test (non-directional)
A test that rejects extreme outcomes in either tail of the distribution
independent measures design
Allows evaluation of the mean difference between two unknown populations using data from two samples
What are the basic characteristics of an independent-measures, or a between-subjects, research study?
An independent-measures study requires a separate sample for each of the treatments or populations being compared.
What is sampling with replacement?
Each individual selected for a sample is returned to the population before the next individual is selected.
Do you know both μ and σ?
If yes - Z test if no - can you estimate μ (if yes then one sample t test)
type I error
Rejecting null hypothesis when it is true (false positive)
Why is sampling with replacement used?
To ensure that the probability of selecting any specific individual stays constant
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?
When σ is unknown
one-tailed test
a hypothesis test in which the research hypothesis is directional, positing either a mean decrease or a mean increase in the dependent variable, but not both, as a result of the independent variable
Cohen's d
a measure of effect size that assesses the difference between two means in terms of standard deviation, not standard error
the alpha level
a small probability value that defines the concept of "very unlikely."
What does a t-test do?
compares mean scores of 2 groups on the same variable to determine the probability that the groups are different
critical region
consists of outcomes that are very unlikely to occur if the null hypothesis is true, where "very unlikely" is defined by the alpha level. A region of the probability distribution which, if the test statistic falls within it, would cause you to reject the null hypothesis
S(M1-M2)
estimated standard error / sample mean difference
type II error
failing to reject a false null hypothesis (false negative)
If you cannot estimate μ, are you examining 2 samples?
if yes - independent measures t test if no - repeated measures t test
s2p
pooled variance
alpha level
probability of rejecting null when null is correct (.05 means 5% risk of concluding a difference exists when it doesnt)
σM
standard deviation of sample means / population standard error
The denominator of the independent-measures t statistic provides an estimate of the
standard distance between a sample mean and the population mean
When the null hypothesis is true, the standard error is the
standard distance between a sample mean and the population mean
sM
standard error of the mean
what does p value measure
statistical significance; probability of obtaining an effect as extreme as the one in your sample data
r squared
the proportion of the total variation in a dependent variable explained by an independent variable percentage of variance accounted for by the IV
The denominator of the t statistic contains
the sample standard deviation , which is different for different samples. The z-score uses the population standard deviation , which is the same for different samples. Therefore, the t statistic has greater variability.
standard error
the standard deviation of a sampling distribution oM
The standard error (sM) provides a measure of
the standard distance between a sample mean and a population mean in the distribution of sample means
The sample variance describes the
variability of the scores in the sample
(b)H₀: μMonitorMonitor = 72; H₁: μMonitorMonitor ≠ 72. α = .05; 2 tailed test, what is the critical region?
z-scores beyond ±1.96.
