Statistics Exam 3: Vocabulary & T/F

k

# of groups

General Notations

All Chapters

Chapter 17

Anova Notations/Vocabulary

Homework 9, Chapter 15 & 17

Chi-Square Test AND Anova Tests

A t curve is bell-shaped like the z curve but is less spread out.

False

For a sample size n, there are n - 1 degrees of freedom associated with the goodness-of-fit test statistic, X^2.

False

If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.

False

The P-value for a hypothesis test concerning the difference in two population proportions is always calculated by finding the area to the right of the test statistic, regardless of the alternative hypothesis.

False

The large sample z test for mu1 - mu2 can be used as long as at least one of the two sample sizes, n1 and n2, is greater than or equal to 30.

False

The number of degrees of freedom of the two-sample t test are the same as the degrees of freedom for the paired t test statistic.

False

The power of a test is the probability of failing to reject the null hypothesis.

False

The statistical methods of analysis of an variance assume equal sample means in the null hypothesis

False

α is called the observed significance level.

False (P-Value is OBSERVED significance level)

Homework 6, Chapter 12

One Sample Hypotheses Test for Population Mean

Homework 5: Chapter 10

One Sample Hypotheses Test for Population Proportion

Chapter 10 & 12

One-Sample Hypothesis Testing Vocabulary

Decision

Reject Ho OR Fail to reject Ho

(x bar, subscript 1, minus x bar subscript 2) is an unbiased statistic that is used to estimate mu1 - mu2.

True

A type II error is made by failing to reject a false null hypothesis.

True

An analysis of variance may be used to test the differences in the means of more than two independent populations.

True

As n grows larger, the mean of the sampling distribution of (x bar) gets closer to the population mean.

True

Determining the table value for the F distribution requires two values for degrees of freedom.

True

For n sufficiently large, the distribution of (x bar minus mu, subscript x bar, over sigma subscript x bar) is approximately a standard normal distribution.

True

It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than α.

True

Small P-values indicate that the observed sample is inconsistent with the null hypothesis.

True

The chi-squared test statistic, x^2, measures the extent to which the observed cell count differ from those expected H subscript zero, is true.

True

The hypothesis (P1=P2) is equivalent to the hypothesis (P1-P2=0).

True

The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true

True

The statistical methods of analysis of variance assume that the populations are normally distributed.

True

Two samples are said to be independent when the selection of the individuals in one sample has no bearing on the selection of those in the other sample.

True

Homework 8, Chapter 13

Two Sample Hypotheses Test for Population Mean AND Matched Pairs Test

Homework 7, Chapter 11

Two Sample Hypotheses Test for Population Proportion

Null hypothesis (Ho)

a claim about the population characteristics that is initially assumed to be true

Hypotheses (Ho & Ha)

a statement/question about the population characteristic

z-test statistic

a value that is computed using sample data that us used to determine the p-value associated with the test

Critical Value

a z-score that is found by shading the rejection region specified by the level of significance

P hat, subscript c

combined sample proportion

df, subscript b

degrees of freedom between (k-1)

df, subscript w

degrees of freedom within (N-k)

SSE

error sum of squares

MSE

mean squared error (SSE/N-k)

MSTr

mean sum of squares (SSTr/k-1)

x-double bar

overall mean

N

overall sample size

sigma

population standard deviation

P

proportion (Probability in Chi-Square test)

x bar

sample mean

x-bar, subscript i

sample mean of each group i

P hat

sample proportion (number of successes over sample size)

n

sample size

n, subscript i

sample size of each group i

s

sample standard deviation

s, subscript i

sample standard deviation

s^2

sample variance

F

test statistic - F ratio (MSTr/MSE)

Uo (mu)

the hypothesized value, the value you believe is true for the population mean

Po

the hypothesized value, the value you believe is true for the population proportion

Level of significance (alpha)

the probability of a Type I Error

P-Value

the probability of observing values more extreme than the test statistic

Alternative hypothesis

the research question (dictates how to shade the z-curve)

Type II Error

the researcher failed to reject the null hypothesis, but the null hypothesis was false

Type I Error

the researcher rejected the null hypothesis, but the null hypothesis was true

The spread of the sample mean decreases when

the sample size is increases.

SSTr

treatment sum of squares

Mu (u)

true mean