Question 1

Hemoglobin level data for three independent groups are associated with the summary statistics reported in the table below.

Given summary statistics in the table, answer questions number 1-5.

Group	Number of Subjects n	Sample Mean	Sample Standard Deviation
1	10	13.0	2.0
2	10	12.0	2.0
3	10	11.0	2.0

An investigator is trying to test hemoglobin level differences in these three populations. The hypothesis are

Group of answer choices

H01=2=3vsHA123

H01=2=3vsHA12or13or23

Flag question: Question 2

The test which is used to test hemoglobin level difference in these three population is

Group of answer choices

z-statistics test

t-statistics test

F-statistics test

Flag question: Question 3

ANOVA is analysis of variance. It requires data to meet certain conditions. The following three conditions are frequently used in statistics tests. 1. Sampling independence within and among groups 2. Normality of sampling distribution of means 3. Equal variances in the source populations The conditions for ANOVA are

Group of answer choices

1 and 2

1 and 3

2 and 3

only 3

all 1, 2 and 3

None of these three conditions

Flag question: Question 4

Pair-wise comparisons among these three groups are called post hoc comparisons. If the ANOVA test fails to reject the null hypothesis in question 1, post hoc comparisons are not needed.

Group of answer choices

True

False

Flag question: Question 5

Post hoc multiple comparisons will increase

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Type I error

Type II error

Both Type I and II errors

None of above

Flag question: Question 6

Given incomplete ANOVA table for Hemoglobin level data below, answer question number 6-10.

	Sum of Squares	df	Mean Square	F-value	P-value
Between Groups	20.0	2
Within Groups	108.0	27
Total	128.0	29

The mean square between groups is

Group of answer choices

20.0

2.5

10.0

4.0

Flag question: Question 7

The mean square within groups is

Group of answer choices

20.0

2.5

10.0

4.0

Flag question: Question 8

The F-value for testing hemoglobin level difference in these three population is

Group of answer choices

20.0

2.5

10.0

4.0

Flag question: Question 9

Given a critical value ofF2,27(0.95)=4.20, the null hypothesis is

Group of answer choices

Reject

Retain

Can not be determined

Flag question: Question 10

The P-value for testing hemoglobin level difference in these three population is

Group of answer choices

Larger than 0.05

Less than 0.05

Can not be determined

Flag question: Question 11

In a research study, descriptive statistics of BMI for three-group and all pair-wise comparisons are summarized in two tables below.

Table I

Group	ni	xibar (mean)	si(standard deviation)
1	8	24	2
2	8	26	2
3	8	28	2

Table II

		Mean Diff	Std Error
(i) group	(j) group	(i-j)	SE
1	2	-2	1
	3	-4	1
2	1	2	1
	3	-2	1
3	1	4	1
	2	2	1

Critical t value and alpha level from Table (C)

t	alpha-level
2.080	0.05

Based on above three tables, please answer the questions 11-25

The t-statistic for mean difference between group 1 and group 2 (group 1 - group 2)

Group of answer choices

2

1

4

-1

-2

-4

Flag question: Question 12

The t-statistic for mean difference between group 1 and group 3 (group 1 - group 3)

Group of answer choices

2

1

4

-1

-2

-4

Flag question: Question 13

The t-statistic for mean difference between group 2 and group 1 (group 2 - group 1)

Group of answer choices

2

1

4

-1

-2

-4

Flag question: Question 14

The t-statistic for mean difference between group 2 and group 3 (group 2 - group 3)

Group of answer choices

2

1

4

-1

-2

-4

Flag question: Question 15

The t-statistic for mean difference between group 3 and group1 (group 3 - group 1)

Group of answer choices

2

1

4

-1

-2

-4

Flag question: Question 16

The two-sided p-value of comparing means between group 1 and group 2

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

Flag question: Question 17

The two-sided p-value of comparing means between group 1 and group 3

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

Flag question: Question 18

The two-sided p-value of comparing means between group 2 and group 1

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

Flag question: Question 19

The two-sided p-value of comparing means between group 3 and group 2

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

Flag question: Question 20

The two-sided p-value of comparing means between group 3 and group 1

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

Flag question: Question 21

95% confidence interval for the mean difference between group 1 and group 2 (group 1- group 2)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

Flag question: Question 22

95% confidence interval for the mean difference between group 1 and group 3 (group 1- group 3)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

Flag question: Question 23

95% confidence interval for the mean difference between group 2 and group 1 (group 2- group 1)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

Flag question: Question 24

95% confidence interval for the mean difference between group 2 and group 3 (group 2- group 3)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

Flag question: Question 25

95% confidence interval for the mean difference between group 3 and group 1 (group 3- group 1)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

Flag question: Question 26

Bonferroni's method ensures that the family-wise error rate is less than or equal to the design level such as 0.05 after all possible pairs-wise comparisons have been made. Three groups have 3 possible pairs-wise comparisons. Four groups have 6 possible pairs-wise comparisons.

Please answer following questions 26-29 based on this method.

A study has three groups. Given an overall design error rate 0.05, a pairs-wise comparison can be claimed statistically significant difference when the p-value less than

Group of answer choices

0.05

0.017

0.15

0.008

0.3

Flag question: Question 27

A study has four groups. Given an overall design error rate 0.05, a pairs-wise comparison can be claimed statistically significant difference when the p-value less than

Group of answer choices

0.05

0.017

0.15

0.008

0.3

Flag question: Question 28

A study has three groups. An investigator wants to claim a statistically significant difference if a pairs-wise comparison p-value less 0.05. The overall design error rate for this study could be as large as

Group of answer choices

0.05

0.017

0.15

0.008

0.3

Flag question: Question 29

A study has four groups. An investigator wants to claim a statistically significant difference if a pairs-wise comparison p-value less 0.05. The overall design error rate for this study could be as large as Group of answer choices

0.05

0.017

0.15

0.008

0.3

Flag question: Question 30

If a study has only two groups, a statistician uses ANOVA to compare means between these two groups, the conclusion from ANOVA is

Group of answer choices

same as two-sample t-test with unequal variance.

same as two-sample t-test with equal variance.

Can not be determined