8.20 The use of computers as an instructional aid is widely advocated as a means to capture the attention of the current computer literate generation of students. A study was designed to assess the effectiveness of using computers as a supplement to the standard mode of instruction. Forty students in an alternative school were randomly assigned to one of four methods of teaching basic math skills. The four methods were lectures only (L), lectures with remedial textbook assistance (L/R), lectures with computer assistance (L/C), and computer instruction only (C). After a 10-week instructional period, an exam evaluating basic math skills was taken by the students. The difference in the scores on this exam and on an exam given just prior to the 10-week instructional period for each student is given in the following table. A few of the students did not complete the program, thus producing an unequal number of students in the four modes of instruction. The researchers want to determine which method of instruction produces the largest increase in test scores. Student Method 1 2 3 4 5 6 7 8 9 10 L 9 2 2 6 16 11 9 0 4 2 L/R 5 2 3 11 16 11 3 L/C 9 12 2 17 12 20 20 31 21 C 17 12 26 1 47 27 -8 10 20 a. Which method of instruction appears to produce the largest gain in scores? b. Is there significant evidence of a difference in the mean gains for the four methods of instruction? c. Do the conditions for conducting statistical tests appear to be satisfied? Justify your conclusions with graphs/tests. d. What is the target population for this study? e. Do the data collected in this study allow inferences to the target population?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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8.20

The use of computers as an instructional aid is widely advocated as a means to capture the attention of the current computer literate generation of students. A study was designed to assess the effectiveness of using computers as a supplement to the standard mode of instruction. Forty students in an alternative school were randomly assigned to one of four methods of teaching basic math skills. The four methods were lectures only (L), lectures with remedial textbook assistance (L/R), lectures with computer assistance (L/C), and computer instruction only (C). After a 10-week instructional period, an exam evaluating basic math skills was taken by the students. The difference in the scores on this exam and on an exam given just prior to the 10-week instructional period for each student is given in the following table. A few of the students did not complete the program, thus producing an unequal number of students in the four modes of instruction.

The researchers want to determine which method of instruction produces the largest increase in test scores.

Student

Method	1	2	3	4	5	6	7	8	9	10
L	9	2	2	6	16	11	9	0	4	2
L/R	5	2	3	11	16	11	3
L/C	9	12	2	17	12	20	20	31	21
C	17	12	26	1	47	27	-8	10	20

a. Which method of instruction appears to produce the largest gain in scores?

b. Is there significant evidence of a difference in the mean gains for the four methods of instruction?

c. Do the conditions for conducting statistical tests appear to be satisfied? Justify your conclusions with graphs/tests.

d. What is the target population for this study?

e. Do the data collected in this study allow inferences to the target population?

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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