Data Analysis Final Part 3

Confidence Interval

provides additional information about the variability of the estimate, provides more information about a population characteristic than a point estimate

Confidence Interval Estimate

gives a range of values, takes into consideration variation in sample statistics from sample to sample, based on observations from 1 sample, gives information about closeness to unknown population parameters, stated in terms of level of confidence (ex. 95% confident)

Impossible Confidence Level

100% confidence

What Confidence Intervals are for

to get to know population parameters when working with sample statistics, it gives you a range of values

Alpha

1 - confidence level = __

(ex. 1 - .95 = .05)

also known as the level of significance

When Standard Deviation is Known …

use the z distribution for the confidence interval

When the Standard Deviation is Unknown …

use the t distribution for the confidence interval

Critical Value

a table value based on the sampling distribution of the point estimate and the desired confidence level

T Distribution

used when the population standard deviation is unknown, relies on degrees of freedom

Degrees of Freedom

n - 1

(n = sample size)

Can Confidence Intervals be used with Categorical Data?

yes, for proportions measuring items of interest in a population

Determining the Required Sample Size for the Mean

you must know the desired level of confidence, the acceptable sampling error, and standard deviation to determine this

Determining the Required Sample Size for the Proportion

you must know the desired level of confidence, acceptable sampling error, and the true proportion of events of interest to determine this

Hypothesis Definition

a claim about a population parameter

What Sign Does the Null Hypothesis Have to Have?

equal sign (=)

Null Hypothesis

begins with the assumption that this hypothesis is true, represents the current belief in a situation, may or may not be rejected

Alternative Hypothesis

challenges the status quo, is generally the hypothesis that the researcher is trying to confirm

If the Null Hypothesis is Rejected …

the alternative hypothesis is NOT proven to be correct

Type I Error Definition

the null hypothesis is true but we rejected it

Probability of Type I Error

alpha

Type II Error Definition

the null hypothesis is false but we did not reject it

When do you reject the null hypothesis?

when the p value is less than the level of significance (alpha)

One Sample t Minitab / T Mean Excel

use when testing the hypothesis of the mean

data needed → null hypothesis, level of significance, sample size, sample mean, sample standard deviation

Two sample t Minitab / Pooled variance t excel

use when testing for differences in two means/variances

data needed → hypothesized difference, level of significance, sample size of both samples, sample mean of both samples, and sample standard deviation of both samples

Paired t test Minitab / Paired t test excel

use in testing means for two related or dependent or same populations

data needed → hypothesized mean difference, level of significance, individual data entries

Two proportions Minitab / Z two proportions excel

use when finding the differences in two proportions

data needed → hypothesized difference, level of significance, number of items of interest for both groups, sample size for both groups

Two variances Minitab / f two variances excel

for numerical data, if two samples are from independent populations, compare variances of each sample

data needed → level of significance, sample size for both samples, sample variance for both samples

When Samples Should be Independent

the samples are from unrelated populations

When the Samples Should be Paired

when the samples are from related populations

Anova One Way

compares three or more means (are they equal or not)

Tukey Kramer

used for to establish significant differences among groups

Chi Square Test

used for multiple groups of people with proportions

Regression

two numerical variances used to predict the y value (quality of variances)

Anova Assumptions

random sample, the distribution is normal, the sample size is greater than 30

Regression Analysis

used to predict the value of a dependent variable based on the value of at least one independent variable (explains the impact of changes in an independent variable on the dependent variable)

Dependent Variance in Regression

y , the variable we wish to predict or explain

Independent Variable in Regression

x , the variable used to predict or explain the dependent variable

Linear Regression Relationship

Curvilinear Regression Relationship

No Regression Relationship

regression is always used on …

two numeric variables.

In regression charts, the dependent variable goes on the _-axis. (enter one lower case letter)

y

in regression charts, the independent variable goes in the _-axis (enter one lower case letter)

x

in regression lines, the R², the coefficient of determination, measures …

how much of the variation in Y can be explained by the variation in X, according to the model, basically how well the points in the scatter plot fit the line (he said it’s the longest one)

In multivariable regression, each independent numerical variance – in minitab these are called “continuous predictors” — that correlates to the dependent variable (the “response” in minitab” gets its own …

slope coefficient