Question

True or False

1) If the alternative hypothesis of an ANOVA F-test is true, we expect MSG to be less than MSE. test

2) An F distribution depends on two differrent degrees of freedom, one for numerator and the other for denominator.

3) If the conditional distributions in a two-way table are similar to each other, one can conclude that the two variables in the two-way table are associated.

4) In a two-way table, if the expected counts are about the same as the observed counts, the P-value of the chi-square statistic is close to zero.

5) In an ANOVA F-test comparing multiple population means, (a) the rejection region is two-tailed. (b) if the null hypothesis is true, MSG is about the same as MSE. (a) and (b) none of the above

6) Consider an ANOVA procedure to compare four population means. Thus, the total number of pairs to be considered in multiple comparisons is six. If the probability that the null hypothesis is falsely rejected in each pair is equal to 0.01, the probability that the null hypothesis is falsely rejected at least once in all six pairs is approximately (Use an approximation formula and give your answer to two decimal places.)

7) Which of the following is not a correct statement regarding the chi-square test associated with a two-way table? A large chi-square statistic supports the alternative hypothesis. A small P-value indicates that the two variables in the table are not associated. The null hypothesis states that the two variables of a two-way table are not associated. It can be used to determine whether or not the proportions of two or more populations are equal. It can be used to examine the relationship between two categorical variables.

Answer 1

Solution2:

TRUE

see below table

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	8.666667	2	4.333333	1.344828	0.308307	4.256495
Within Groups	29	9	3.222222
Total	37.66667	11

df for numerator=Between groups

df for Denominator=within groups

4) In a two-way table, if the expected counts are about the same as the observed counts, the P-value of the chi-square statistic is close to zero.

if O=E

chi sq=total(O-E)^2/E=0

sample data

0	E
25	25
45	45
56	56
7	7

df=(2-1)(2-1)

df=1

p=1

p>0.05

p not equal to 0 its equal to 1.

FALSE

Solution7:

H0:both varaibles are independent

H1:both variables are dependent(assocaited)

A small P-value indicates that the two variables in the table are not associated

p<0.05

REJECT H0

Accept H1

MEANS TWO VARIABLES ARE ASSOCIATED

SO GIVEN STATEMENT IS FALSE

A small P-value indicates that the two variables in the table are not associated.