Exhibit 7-12: An investigator is studying the effect of two physical fitness programs (M and N) on boys and girls.The experimental design is a 2 * 2 factorial design.The results of the investigation might be one of the following four conditions. $\begin{array}{l} \begin{array}{lll} &\text { Condition (a)}\\ &\mathrm{M} & \mathrm{N} \\ \text { Boys }&\mathrm{X}=50 & \mathrm{X}=60 \\ \text { Girls }&\mathrm{X}=60 & \mathrm{X}=50 \end{array} \begin{array}{lll} &\text { Condition (b)}\\ &\mathrm{M} & \mathrm{N} \\ \text { Boys }&\mathrm{X}=50 & \mathrm{X}=60 \\ \text { Girls }&\mathrm{X}=40 & \mathrm{X}=60 \end{array} \end{array}$ $\begin{array}{l} \begin{array}{lll} &\text { Condition (c)}\\ &\mathrm{M} & \mathrm{N} \\ \text { Boys }&\mathrm{X}=50 & \mathrm{X}=40 \\ \text { Girls }&\mathrm{Y}=60 & \mathrm{Y}=50 \end{array} \begin{array}{lll} &\text { Condition (d)}\\ &\mathrm{M} \quad\quad\quad\quad\quad\quad\quad\quad \mathrm{N} \\ &\text { None of these condition }\\ \\ \end{array} \end{array}$ -What is the relationship between the standard deviation of a population and the standard deviation of means of samples randomly selected from the population?

A) The standard deviation of the distribution of sample means is larger than that of the population. B) The standard deviation of the population is larger than that of the distribution of sample means. C) They are equal to one another. D) It is impossible to determine the relationship with the available data. A) The standard deviation of the distribution of sample means is larger than that of the population. B) The standard deviation of the population is larger than that of the distribution of sample means. C) They are equal to one another. D) It is impossible to determine the relationship with the available data.

Exhibit 7-11: In a 2 $\times$ 3 experimental design three kinds of treatments (A, B, and C) were used with two groups of subjects (M and N).The number of subjects and the mean of each group are as follows: $\begin{array}{lll} &&&\text { Treatments }\\ &&\mathrm{A} & \mathrm{B} & \mathrm{C} \\ &\mathrm{~M}&\mathrm{X}=20 & \mathrm{X}=18 & \mathrm{X}=16 \\ &&\mathrm{~N}=5 & \mathrm{~N}=5 & \mathrm{~N}=5 \\ \text { subjects } \\ &\mathrm{~N}&\mathrm{X}=12 & \mathrm{X}=14 & \mathrm{X}=16 \\ &&\mathrm{~N}=5 & \mathrm{~N}=5 & \mathrm{~N}=5 \end{array}$ The following is the incomplete summary table of multifactor analysis of variance.Complete the table and answer the following questions. $\begin{array}{ll} \text { Source of variation } & S S & \underline { \text { df }} & \underline { \text { MS}} & \underline { \text { F}}\\ \hline \text { Between columns } & 0 \\ \text { Between rows } & 120 \\ \text { Interaction } & \\ \hline \text { Between groups } & 200 \\ \text { Within groups } & \\ \hline \text { Tntal } & 454 \end{array}$ -Refer to Exhibit 7-11.The F ratio for interaction is

A) 0. B) 11.38. C) 3.78. D) None of these. A) 0. B) 11.38. C) 3.78. D) None of these.

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group. $ \begin{array}{lll}\text { Morning } & {\text { Old }}{} & {\text { New }}{} \\ & 16.33 & 13.50 \\ &1.03 & 2.74 \\& 6 & 6 \\ \text { Afternoon } & 13.17 & 16.83 \\ & 3.55 & 2.14 \\ & 6 & 6\end{array} $ The following is an incomplete summary table of the analysis of variance: $\begin{array}{ll} \underline { \text { Source }} & \underline { \text { SS }} & \underline { \text { df }} & \underline { \text { MS}} & \underline { \text { F}}\\ \text { Time of Day } & 0.042 \\ \text { Lesson Design } & 1.042 \\ \text { Interaction }\\ \text { Error } & 128.500 \\ \text { Total } & 102950 \end{array}$ -Refer to Exhibit 7-7.Which sources of variance are significant?

A) Time of Day B) Lesson Design C) Interaction D) a and b E) None of these are true. A) Time of Day B) Lesson Design C) Interaction D) a and b E) None of these are true.

Exhibit 7-11: In a 2 $\times$ 3 experimental design three kinds of treatments (A, B, and C) were used with two groups of subjects (M and N).The number of subjects and the mean of each group are as follows: $\begin{array}{lll} &&&\text { Treatments }\\ &&\mathrm{A} & \mathrm{B} & \mathrm{C} \\ &\mathrm{~M}&\mathrm{X}=20 & \mathrm{X}=18 & \mathrm{X}=16 \\ &&\mathrm{~N}=5 & \mathrm{~N}=5 & \mathrm{~N}=5 \\ \text { subjects } \\ &\mathrm{~N}&\mathrm{X}=12 & \mathrm{X}=14 & \mathrm{X}=16 \\ &&\mathrm{~N}=5 & \mathrm{~N}=5 & \mathrm{~N}=5 \end{array}$ The following is the incomplete summary table of multifactor analysis of variance.Complete the table and answer the following questions. $\begin{array}{ll} \text { Source of variation } & S S & \underline { \text { df }} & \underline { \text { MS}} & \underline { \text { F}}\\ \hline \text { Between columns } & 0 \\ \text { Between rows } & 120 \\ \text { Interaction } & \\ \hline \text { Between groups } & 200 \\ \text { Within groups } & \\ \hline \text { Tntal } & 454 \end{array}$ -Refer to Exhibit 7-11.The SS within the groups is

A) 54. B) 200. C) 254. D) None of these. A) 54. B) 200. C) 254. D) None of these.

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group. $ \begin{array}{lll}\text { Morning } & {\text { Old }}{} & {\text { New }}{} \\ & 16.33 & 13.50 \\ &1.03 & 2.74 \\& 6 & 6 \\ \text { Afternoon } & 13.17 & 16.83 \\ & 3.55 & 2.14 \\ & 6 & 6\end{array} $ The following is an incomplete summary table of the analysis of variance: $\begin{array}{ll} \underline { \text { Source }} & \underline { \text { SS }} & \underline { \text { df }} & \underline { \text { MS}} & \underline { \text { F}}\\ \text { Time of Day } & 0.042 \\ \text { Lesson Design } & 1.042 \\ \text { Interaction }\\ \text { Error } & 128.500 \\ \text { Total } & 102950 \end{array}$ -Refer to Exhibit 7-7.What are the degrees of freedom for Lesson Design?

A) 1 B) 2 C) 20 D) 24 A) 1 B) 2 C) 20 D) 24

Exam 7: Sampling and Inferential Statistics

Exhibit 7-12: An investigator is studying the effect of two physical fitness programs (M and N) on boys and girls.The experimental design is a 2 * 2 factorial design.The results of the investigation might be one of the following four conditions. Condition (a) Boys =50 =60 Girls =60 =50 Condition (b) Boys =50 =60 Girls =40 =60 Condition (c) Boys =50 =40 Girls =60 =50 Condition (d) None of these condition -What is the relationship between the standard deviation of a population and the standard deviation of means of samples randomly selected from the population?

(Multiple Choice)

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Question 101

Exhibit 7-11: In a 2 $\times$ 3 experimental design three kinds of treatments (A, B, and C) were used with two groups of subjects (M and N).The number of subjects and the mean of each group are as follows: Treatments =20 =18 =16 =5 =5 =5 subjects =12 =14 =16 =5 =5 =5 The following is the incomplete summary table of multifactor analysis of variance.Complete the table and answer the following questions. Source of variation SS Between columns 0 Between rows 120 Interaction Between groups 200 Within groups Tntal 454 -Refer to Exhibit 7-11.The F ratio for interaction is

(Multiple Choice)

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Question 102

Exhibit 7-5: A researcher finds a .40 correlation between the number of years a student has access to a computer and his or her attitude toward mathematics.The study used 20 subjects. -Refer to Exhibit 7-5.A correlation that is not statistically significant leads to the conclusion that:

(Multiple Choice)

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Question 103

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group. Morning Old New 16.33 13.50 1.03 2.74 6 6 Afternoon 13.17 16.83 3.55 2.14 6 6 The following is an incomplete summary table of the analysis of variance: Time of Day 0.042 Lesson Design 1.042 Interaction Error 128.500 Total 102950 -Refer to Exhibit 7-7.Which sources of variance are significant?

(Multiple Choice)

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Question 104

Exhibit 7-11: In a 2 $\times$ 3 experimental design three kinds of treatments (A, B, and C) were used with two groups of subjects (M and N).The number of subjects and the mean of each group are as follows: Treatments =20 =18 =16 =5 =5 =5 subjects =12 =14 =16 =5 =5 =5 The following is the incomplete summary table of multifactor analysis of variance.Complete the table and answer the following questions. Source of variation SS Between columns 0 Between rows 120 Interaction Between groups 200 Within groups Tntal 454 -Refer to Exhibit 7-11.The SS within the groups is

(Multiple Choice)

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Question 105

Exhibit 7-6: A group of researchers hypothesizes that listening to music while studying for an exam influences test scores.They randomly selected 28 subjects and divided them into four groups.All groups studied silently for a test for an hour a day for a week.Group 1 studied without music.Group 2 studied with classical music in the background, Group 3 with country, and Group 4 with jazz.The following are the final test scores: Group 1 Group 2 50 59 45 57 42 57 41 55 40 56 39 53 38 51 Group 3 Group 4 60 49 56 45 56 45 55 42 54 41 51 39 50 37 -Refer to Exhibit 7-6.What is the null hypothesis?

(Multiple Choice)

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Question 106

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group. Morning Old New 16.33 13.50 1.03 2.74 6 6 Afternoon 13.17 16.83 3.55 2.14 6 6 The following is an incomplete summary table of the analysis of variance: Time of Day 0.042 Lesson Design 1.042 Interaction Error 128.500 Total 102950 -Refer to Exhibit 7-7.What are the degrees of freedom for Lesson Design?

(Multiple Choice)

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Question 107

Exhibit 7-3: A researcher is examining the effects of a computer-based training program designed to teach algebra.The researcher randomly selects subjects for two groups and gives one group the computer training and the other standard teaching methods to see if the results of the two methods differ.The following scores are from the subjects' final test. CBT Control 52 65 55 45 56 47 53 46 50 47 49 33 52 39 53 49 -Refer to Exhibit 7-3.What is the null hypothesis?

(Multiple Choice)

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Question 108

Exhibit 7-4: A group of researchers has developed a method that they hypothesize will improve physics test scores.They randomly selected nine students to participate in their study.The nine students were administered an ACT test, trained in the new method, and then administered an alternate form of the ACT test.The following data are their scores: Subject Test 1 Test 2 1 20 19 2 20 20 3 24 21 4 24 24 5 24 22 6 17 15 7 18 15 8 18 16 9 20 18 -Refer to Exhibit 7-4.What is the observed value for the chosen statistic?

(Multiple Choice)

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Question 109

Exhibit 7-6: A group of researchers hypothesizes that listening to music while studying for an exam influences test scores.They randomly selected 28 subjects and divided them into four groups.All groups studied silently for a test for an hour a day for a week.Group 1 studied without music.Group 2 studied with classical music in the background, Group 3 with country, and Group 4 with jazz.The following are the final test scores: Group 1 Group 2 50 59 45 57 42 57 41 55 40 56 39 53 38 51 Group 3 Group 4 60 49 56 45 56 45 55 42 54 41 51 39 50 37 -Refer to Exhibit 7-6.The test is statistically significant at what level?

(Multiple Choice)

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Question 110

Exhibit 7-5: A researcher finds a .40 correlation between the number of years a student has access to a computer and his or her attitude toward mathematics.The study used 20 subjects. -Refer to Exhibit 7-5.What are the degrees of freedom in this case?

(Multiple Choice)

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Question 111

Exhibit 7-2: Label the following characteristics of sampling procedures as convenience, purposive, or quota. -Refer to Exhibit 7-2.Weakest of all sampling procedures.

(Multiple Choice)

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Question 112

What is the difference between Type I and Type II errors?

(Short Answer)

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Question 113

Exhibit 7-5: A researcher finds a .40 correlation between the number of years a student has access to a computer and his or her attitude toward mathematics.The study used 20 subjects. -Refer to Exhibit 7-5.A correlation that is not statistically significant leads to the conclusion that:

Exhibit 7-5: A researcher finds a .40 correlation between the number of years a student has access to a computer and his or her attitude toward mathematics.The study used 20 subjects. -Refer to Exhibit 7-5.What are the degrees of freedom in this case?

Exhibit 7-2: Label the following characteristics of sampling procedures as convenience, purposive, or quota. -Refer to Exhibit 7-2.Weakest of all sampling procedures.

What is the difference between Type I and Type II errors?

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