Unit 7: Statistical Inference

Degrees 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