Statistic Procedures (Except the proportion tests)

What is a One Sample T-Test

What is a One Sample T-Test

Used to test a claim about a population mean

Null Hypothesis for One Sample T-Test

μ = #

Alternate Hypothesis for One Sample T-Test

μ > #
μ < #
μ ≠ #

Conditions for One Sample T-Test

1) Sample is random
2) Sampling distribution is approximately normal ( a. If n≥30 , assumed by CLT b. if n≤30 this condition needs to be checked with a histogram)

What is in the Calculation step of a One Sample T-Test

T-value, P-Value and Degrees of Freedom

Formula for One Sample T-Test

Calculator: Stats, Tests, 2

Formula for Degrees of Freedom in a One Sample T-Test

df = n-1

Conclusion for One Sample T-Test

Since the P-value of ___ is less than/greater than the α-level of .05, we reject/fail to reject the H0. In other words, there is/isn’t statistically significant evidence to support the HA that ___ (context)

What is a One Sample T-Interval?

Used to give a plausible range of values for population mean

Conditions for One Sample T-Interval

1) Sample is random
2) Sampling distribution is approximately normal ( a. If n≥30 , assumed by CLT b. if n≤30 this condition needs to be checked with a histogram)

What is needed for the Calculation step of a One Sample T-Interval

Range of values, Degrees of Freedom

Formula for One Sample T-Interval

Calculator: Stats, Tests, 8

Formula for Degrees of Freedom in a One Sample T-Interval

df = n-1

Conclusion for One Sample T-Interval

We are ___% confident that the true mean of ___ (context) lies between ___(lower bound) and ___(upper bound) ___ (units)

What is a Two Sample T-Test

Used to test a claim about a difference of population means

Null Hypothesis for Two Sample T-Test

H0: μ1 = μ2

Alternate Hypothesis for Two Sample T-Test

μ1 > μ2
μ1 < μ2
μ1 ≠ μ2

What is needed in the Calculation Step of a Two Sample T-Test

T-Value, P-Value and Degrees of Freedom

Formula for Two Sample T-Test

Calculator: Stats, Tests, 4,

Conclusion for Two Sample T-Test

Since the P-value of ___ is less than/greater than the α-level of .05, we reject/fail to reject the H0. In other words, there is/isn’t statistically significant evidence to support the HA that ___ (context)

What is a Two Sample T-Interval

Used to give a plausible range of values for a difference in population means

Conditions for a Two-Sample T-Interval

1) Sample are random and independent
2) Sampling distributions are approximately normal ( a. If n1,n2≥30, assumed by CLT b. if n1,n2≤30 this condition needs to be checked with a histogram(s)

What is needed in the Calculation step of a Two Sample T-Interval

T-Value, P-Value and Degrees of Freedom

Formula for Two Sample T-Interval

Calculator: Stats, Tests, 0

Conclusion for Two Sample T-Interval

We are ___% confident that the true difference in the mean of ___ (context) lies between ___(lower bound) and ___(upper bound) ___

What is a Paired T-Test

Used to test a claim about a difference population means for dependent data

Null Hypothesis for Paired T-Test

μd = 0

Alternate Hypothesis for Paired T-Test

μd > 0
μd < 0
μd ≠ 0

Conditions for Paired T-Test

1) Matched Pairs Design: Subjects are randomly assigned treatments
Repeated Measures Design: The order in which subjects received treatments was random
Sample is random (sample, not experiment)

2) Sampling Distribution of differences is approximately normal

What do you need for the Calculation step of a Paired T-Test

T-Value, P-value, and Degrees of Freedom

Formula for Paired T-Test

Calculator: Stats, Tests, 2

Formula for Degrees of Freedom in a Paired T-Test

df = n-1

Conclusion for Paired T-Test

Since the P-value of ___ is less than/greater than the α-level of .05, we reject/fail to reject the H0. In other words, there is/isn’t statistically significant evidence to support the HA that ___ (context)

What is a Paired T-Interval

Used to give a plausible range of values for the difference in population means for dependent data

Conditions for a Paired T-Interval

1) Matched Pairs Design: Subjects are randomly assigned treatments
Repeated Measures Design: The order in which subjects received treatments was random
Sample is random (sample, not experiment)

2) Sampling Distribution of differences is approximately normal

What is needed for the Calculation step of a Paired T-Interval

Range of values and Degrees of Freedom

Formula for Paired T-Interval

Calculator: Stats, Tests, 8

Formula for Degrees of Freedom in a Paired T-Interval

df = n-1

Conclusion for Paired T-Interval

We are ___% confident that the true differences in the mean of ___ (context) lies between ___(lower bound) and ___(upper bound) ___

What is a X² Goodness of Fit Test

Used to test a claim that the proportions of a single categorical variable are consistent with some expectation

Null Hypothesis for X² Goodness of Fit Test

The data is consistent with what we expect

Alternate Hypothesis for X² Goodness of Fit Test

The data is no consistent with what we expect

Conditions for X² Goodness of Fit Test

1) Sample is random
2) Expected frequencies are at least 5 (Create a table with Observed and Expected, computed using the given proportions/ratios for the sub-categories)

What is needed for the Calculation step of a X² Goodness of Fit Test

X² Value, P-value, and Degrees of Freedom

Formula for X² Goodness of Fit Test

Calculator: Stats, Tests, D

Formula for Degrees of Freedom in a X² Goodness of Fi

df = n-1

Conclusion for X² Goodness of Fit Test

Since the P-value of ___ is less than/greater than the α-level of .05, we reject/fail to reject the H0. In other words, there is/isn’t statistically significant evidence to support the HA that ___ (context)

What is a X² Independence Test

Used to test if two categorical variables are independent of one another

Null Hypothesis for X² Independence Test

There is no association between ___ and ___

Alternate Hypothesis for X² Independence Test

There is an association between ___ and ___

Conditions for X² Independence Test

1) Sample is Random
2) Expected Frequencies are at least 5 | (row total*column total)/grand total

What is needed for the Calculation step of the X² Independence Test

X² Value, P-Value, and Degrees of Freedom

Formula for X² Independence Test

Calculator: Stats, Tests, C

Formula for Degrees of Freedom of a X² Independence Test

df = (r-1)(c-1)

Conclusion for X² Independence Test

Since the P-value of ___ is less than/greater than the α-level of .05, we reject/fail to reject the H0. In other words, there is/isn’t statistically significant evidence to support the HA that ___ (context)

What is a X² Homogeneity Test

Used to test if the distribution of the sub-categories of a single categorical variable is the same for multiple populations

Null Hypothesis for X² Homogeneity Test

The distribution of ___ is the same for ___ and ___

Alternate Hypothesis for X² Homogeneity Test

The distribution of ___ is not the same for ___ and ___

Conditions for X² Homogeneity Test

1) Samples are random and independent
2) Expected frequencies are at least 5 (row total*column total)/grand total

What do you need for the Calculation step of the X² Homogeneity Test

X² Value, P-value, Degrees of Freedom

Formula for X² Homogeneity Test

Calculator: Stats, Tests, C

Formula for Degrees of Freedom for X² Homogeneity Test

df = (r-1)(c-1)

Conclusion for X² Homogeneity Test

Since the P-value of ___ is less than/greater than the α-level of .05, we reject/fail to reject the H0. In other words, there is/isn’t statistically significant evidence to support the HA that ___ (context)