Studied by 11 peopleDegrees of freedom
________: which depends on how chi- square is being used.
Ho
________: The distributions of the two populations are the same.
Homogeneity
________: decides if two populations with unknown distributions have the same distribution as each other.
Alternative Hypothesis
________ (Ha): A statement that we are trying to find evidence to support; contradictory to H0.
Unbiasedness
________: the idea that a statistic is expected to give values centered on the unknown parameter value.
Conclusion
________: conclude your results based on your interval with context.
Ha
________: The distributions of the two populations are not the same.
margin of error
The ________: how many percentages points your results will differ from the real population value.
Independence
________: decides whether two variables are ________ or dependent.
Bias
________: the difference between the estimated probability and the true value of the parameter being estimated.
measurements
Two ________ (samples) are drawn from the same pair of individuals or objects.
Correlation coefficient
________ (r): is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
Left
________- tailed tests:"too small "values of the statistic as compared to the hypothesized parameter value lead to the rejection of the null hypothesis.
Parameter
________: characteristic of a population.
Inefficiency
________: indicates that our guess is wrong unsystematically.
test statistic
The ________: Measures the difference between the sample result and the null value.
RR
Rejection or critical region (________ or CR): the set of test statistic values for which we should reject the null hypothesis.
GOF
Ha for ________: The population does not fit the given distribution.
Large test statistic
________: Observed values and corresponding expected values are not close to each other.
Estimation process
________: procedure of guessing an unknown parameter value using the observed values from samples.
Null Hypothesis
________ (H0): A statement of no change, no effect, or no difference.
Parameter of interest
________: state what it is you are interested in with the context.
Confidence interval
________: an interval estimate for an unknown population parameter.
Hypothesis
________: a statement (or claim) about a property /characteristic of a population.
Ho of Homogeneity
________: The two populations follow the same distribution.
Parameter
characteristic of a population
Statistic
number computed from the sample
Estimation process
procedure of guessing an unknown parameter value using the observed values from samples
Estimate
specific guess or value computed from a sample
Point estimate
a single number computed from a sample and used to estimate a population parameter
The margin of error
how many percentages points your results will differ from the real population value
Unbiasedness
the idea that a statistic is expected to give values centered on the unknown parameter value
Bias
the difference between the estimated probability and the true value of the parameter being estimated
Variability
the degree of variation in statistics values
Inefficiency
indicates that our guess is wrong unsystematically
Confidence interval
an interval estimate for an unknown population parameter
Confidence level
considered the probability that the calculated confidence interval estimate will contain the true population parameter
Confidence level interpretation
"We estimate with % confidence that the true population mean (include the context of the problem) is between and (include appropriate units)."
Hypothesis
a statement (or claim) about a property/characteristic of a population
Hypothesis testing
a procedure, based on sample evidence and probability, for testing claims about a property/characteristic of a population
Null Hypothesis (H0)
A statement of no change, no effect, or no difference
Alternative Hypothesis (Ha)
A statement that we are trying to find evidence to support; contradictory to H0
The test statistic
Measures the difference between the sample result and the null value
p-value
the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample
Large p-value
calculated from the data indicates that we should not reject the null hypothesis
Smaller the p-value
the more unlikely the outcome, and the stronger the evidence is against the null hypothesis
Type I error
We reject the null hypothesis when the null hypothesis is true
α
P(Type I Error) = P(Rejecting H0 when H0 is true)
Type II error
We do not reject the null hypothesis when the alternative hypothesis is true
β
P(Type II Error) = P(Failing to Reject H0 when H0 is false)
Left-tailed tests
"too small" values of the statistic as compared to the hypothesized parameter value lead to the rejection of the null hypothesis
Right-tailed tests
"too-large" values of the statistic as compared to the hypothesized parameter a=value lead to the rejection of the null hypothesis
Rejection or critical region (RR or CR)
the set of test statistic values for which we should reject the null hypothesis
Non-rejection region
the set of test statistic values for which we should fail to reject the null hypothesis
Critical value (CV)
the value of a test statistic that gives the boundary between the rejection and the non-rejection region
Parameter of interest
state what it is you are interested in with the context
Assumptions and conditions
check them fro the proper interval you are about to use
Name the type of interval
state the name of the interval that youre about to set up
Interval
perform your calculations and set up the interval
Conclusion
conclude your results based on your interval with context
p-value ≤ α
we reject the null hypothesis
p-value > α
we fail to reject the null hypothesis
If you Reject H0
There is sufficient evidence to conclude [statement in Ha]
If you Fail to Reject H0
There is not sufficient evidence to conclude [statement in Ha]
Parameter of interest
state what it is you are interested in with the context
Hypothesis
State your null and alternative hypothesis
Least-Squares Line
You have a set of data whose scatter plot appears to "fit" a straight line
Least-squares regression line
Helps obtain a line of best fit
Absolute value of a residual
measures the vertical distance between the actual value of y and the estimated value of y
Slope equation
b = r (sy / sx)
Interpretation of the Slope
"The slope of the best-fit line tells us how the dependent variable (y) changes for every one unit increase in the independent (x) variable, on average."
Correlation coefficient (r)
is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y
Degrees of freedom
which depends on how chi-square is being used
Population mean
μ = df
The null and alternative hypotheses for GOF
may be written in sentences or may be stated as equations or inequalities
Null hypothesis
The observed values of the data values and expected values are values you would expect to get
Large test statistic
Observed values and corresponding expected values are not close to each other
Expected value rule
Needs to be above 5 to be able to use the test
Test of independence
Determines whether two factors are independent or not
The null hypothesis for independence
states that the factors are independent
The alternative hypothesis for independence
states that they are not independent (dependent)
Expected value formula
(row total)(column total) / total number surveyed
Test for Homogeneity
used to draw a conclusion about whether two populations have the same distribution
Goodness-of-Fit
decides whether a population with an unknown distribution "fits" a known distribution
Ho for GOF
The population fits the given distribution
Ha for GOF
The population does not fit the given distribution
Independence
decides whether two variables are independent or dependent
Ho for Independence
The two variables (factors) are independent
Ha for Independence
The two variables (factors) are dependent
Homogeneity
decides if two populations with unknown distributions have the same distribution as each other
Ho of Homogeneity
The two populations follow the same distribution
Ha of Homogeneity*
The two populations have different distributions
Note
Flashcard