DSOM 309 Test 1

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Identify the formula used to construct a 100% confidence interval for ratio of pop variances

([s/s] 1/fa/2 ; [s/s] fa/2)

Degrees of Freedom for a CONTIGENCY TABLE is calculated as

(r-1)(c-1) 3 rows 2 columns (3-1)(2-1) = 2

the area to the left of X²a,df value is

1-a

what do we do to find F1-a and why

1/Fa(df2,df1) easier

in a 2-way ANOVA without interaction there are ___ null hypotheses tested

2

in a 2-way ANOVA with interaction there are ____ null hypotheses tested

3

Statistical inference concerning POPULATION VARIANCE is based on

Chi-Square

if two independent samples are drawn from normal populations, then teh value of the test statistic S^21/S^22 follows the

F df1,df2 Distribution

MSB/MSE

F test stat for 2 way anova

A one-way anova test is based on

Fdf1,df2 distribution

the null and alternative hypotheses for a right tailed test concerning pop variance are

Ho: @²≤@²o ; Ha:@²>@²o

null and alternate for Test of Independence

Ho: Are independent Ha: Are dependent

The null and alternative hypotheses for a GOODNESS OF FIT TEST are

Ho: Data are normal Ha: Data are not normal

what are the hypothesis of a one-way ANOVA

Ho: mean = mean = mean Ha: not all means are equal

in a two-way anova the F test statistic that determines whether differences exist between factor A means is calculated as

MSA/MSE

in two-way anova F test stat for Factor A =

MSA/MSE

The GOODNESS OF FIT test for normality is which tailed test

Right Tailed Test

SST in a 2-way ANOVA is equal to

SSA + SSB + SSE

error sum of squares

SSE weighted sum of sample variances of each trements

MSE =

SSE/(nT-c)

one-way ANOVA MSTR =

SSTR/(c-1)

in a two-way ANOVA test, SST for factor B is based on

Sum of squared differences BETWEEN the mean for each level of factor B and the GRAND MEAN

Properties of Estimators

Unbiasedness Efficiency Consistency

The null hypothesis for Jarque-Bera is a joint hypothesis that the Skewness Coeffiecient (S) and the Kurtosis Coefficient (K) are equal to

Zero

a kurtosis coefficient of ZERO means that the distribution is

as peaked as the normal distribution

confidence interval is based on

chi-square distribution

a test of independence is also called a

chi-square test of a contingency table

thhe chi-square distribution tends to the normal distribution as the

degrees of freedom gets larger

in two-way ANOVA the F test statistic for FACTOR B

determines whether significant differences exist between factor b means calculated as: MSB/MSE

ANOVA is used to determine if

differences exist between the means of 3 or more populations

X²df has the following characteristics

distribution is positively skewed distribution range from zero to infinity shapes depend on degrees of freedom

in a two tailed test if the p-value for the hypothesis test is GREATER THAN the chosen level of signicance then

do not reject Ho: population variance does not differ from Ho value since p - value = .068 > .05 = a do not reject

In a MULTINOMIAL EXPERIMENT with null Ho:p1=p2=p3=p4= .25 Value of the TEST STAT is X²₃=3.45 at the a = .05 the CRITICAL VALUE is X²₀.₀₅,₃ = 7.815 the decision rule is

do not reject Ho; cannot conclude populations differ from .25 since Test < Critical Value do not reject

In a TEST OF INDEPENDENCE if the test statistic is LESS THAN the Critical value we X²₁<X²₀.₀₅,1

do not reject Ho; cannot conclude that___ and ___ are dependent

GOODNESS OF FIT TEST for normality with a null Ho: data is normal with µ=10 and @=2 Test Statistic is 4.34 p-value is 0.1143 at the a = .05 the decision is

do not reject Ho; conclude that does follow normal distribution since the p-value = 0.1142 > .05

in ANOVA testing, if the ratio of between-treatment variability to within-treatment is significantly GREATER THAN 1

if between/within is >>>> 1 reject Ho: conclude that not all means are equal

the width of the interval

increases with the confidence level

in order to express the competing hypotheses for a GOODNESS-OF-FIT test for normality we specify the populations

mean standard deviation

when doing F distribution place the larger sample variance in the

numerator

TEST OF INDEPENDENCE compares each cells

observed frequency with expected frequency

assumptions for performing a ONE-way ANOVA

populations are normally distributed populations standard deviations are UNKNOWN but presumed equal the samples are selected independently

what skew is the chi-square distribution

positively

In a right tailed test if the test statistic is greater than the critical value

reject Ho test > crit reject and conclude that pop variance is greater than

If the hypothesized value of pop variance (@²=10) is not included in the confidence interval ([15,20]), we

reject Ho and concluded that pop variance differs

TEST OF INDEPENDENCE if the p-value is LESS THAN the a value

reject Ho: conclude are dependent reject and conclude

In a TEST OF INDEPENDENCE if the test statistic is X²₁ (5.75) GREATER THAN the critical value X²₀.₀₅,₁(3.41) then the decision is

reject Ho: conclude that ___ and ___ are DEPENDENT since X²₁ = 5.75 > 3.851 = X²₀.₀₅,₁ reject , dependent

in an ANOVA table if the p-value is LESS THAN the significance value (a) then

reject Ho: conclude that some means differ

In a two tailed test if the p-value is LESS THAN the significance value (a) then:

reject Ho: population variance differs since p-value = .027 < .05 = a we reject Ho conclude they do differ

for a X²df distributed random variable, the notation X²a,df represents a value such that the area in the

right taile of distribution is a

one-way anova is always which tail

right tailed

when conducting hypothesis test with pop variance the TEST STATISTIC depends on

sample size hypothesized value of pop variance sample variance X²df = (n-1)s²/@₂ = Test Statistic for population variance

the estimator of population variance is

sample variance or S²

a is the

signifacant value percentage

The Jarque-Bera TEST STATISTIC depends on the

skewness coefficient (S) Kurtosis Coefficient (K) Sample Size

in a two-way anova what is used to calculate sst

ssa + ssb + ssab + sse

in a ANOVA test GRAND MEAN is calculated as

sum of all observations divided by total # of observations

in ONE-way ANOVA SSTR =

sum of weighted squared differences between the samples mean and grand mean

a skewness coefficient of ZERO means that the data are

symetric about the mean

The chi-square test of contingency table is valid when

the expected cell frequencies are: at least five ≥5

the chi-square test of a CONTINGENCY TABLE is a test of independence for

two Qualitative variables

a 2-way ANOVA examines the effect of

two factors on the population mean

a one-way anova test helps reduce the risk of what type of error

type 1 error

in a one-way ANOVA within-treatments variability is based on the

variability within each sample a weighted sum of sample variances of each treatment

randomized block with NO interaction if the p-value is less than the a value then

we cannot conclude that the row means differ

in a randomized block experiment if the p-value is LESS THAN the significance level (a) then

we cannot conlude that they differ reject Ho:????

if the F number for interaction is LESS THAN a then

we conclude that there IS interaction

Values of Fdf1,df2 distribution range from

zero to infinity


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