A paper reported that for a group of 76 college students, the average number of responses changed from the correct answer to an incorrect answ multiple-choice items was 0.9. The corresponding standard deviation was reported to be 1.0. Based on this mean and standard deviation, what ca of the distribution of the variable number of answers changed from right to wrong? Since the mean of the distribution is 0.9 answers changed and the standard deviation is 1.0 answers changed, 0 answers changed is 0.9 ✔ standard deviations below the mean. If the distribution were approximately normal, then we would expect about 16% change fewer than 0 answers. Thus the distribution cannot ✔ be well approximated by a normal curve. There must be some values mor ✓ answers changed. This suggests that the distribution is positively: 1 standard deviation above the mean, that is, values above 1.9 How many standard deviations above the mean is three answers changed? 2.1 What can you say about the total number of students who changed at least three answers from correct to incorrect? (Round your answer down to number.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
100%

please help, 1 isn't right for the last question

A paper reported that for a group of 76 college students, the average number of responses changed from the correct answer to an incorrect answer on a test containing 78
multiple-choice items was 0.9. The corresponding standard deviation was reported to be 1.0. Based on this mean and standard deviation, what can you tell about the shape
of the distribution of the variable number of answers changed from right to wrong?
of the students to
Since the mean of the distribution is 0.9 answers changed and the standard deviation is 1.0 answers changed, 0 answers changed is
0.9
standard deviations below the mean. If the distribution were approximately normal, then we would expect about 16%
change fewer than 0 answers. Thus the distribution cannot
be well approximated by a normal curve. There must be some values more than
answers changed. This suggests that the distribution is positively skewed
1 standard deviation above the mean, that is, values above 1.9
î
How many standard deviations above the mean is three answers changed?
2.1
What can you say about the total number of students who changed least three answers from correct to incorrect? (Round your answer dow to the nearest whole
number.)
At most 1
X students changed at least three answers from correct to incorrect.
Transcribed Image Text:A paper reported that for a group of 76 college students, the average number of responses changed from the correct answer to an incorrect answer on a test containing 78 multiple-choice items was 0.9. The corresponding standard deviation was reported to be 1.0. Based on this mean and standard deviation, what can you tell about the shape of the distribution of the variable number of answers changed from right to wrong? of the students to Since the mean of the distribution is 0.9 answers changed and the standard deviation is 1.0 answers changed, 0 answers changed is 0.9 standard deviations below the mean. If the distribution were approximately normal, then we would expect about 16% change fewer than 0 answers. Thus the distribution cannot be well approximated by a normal curve. There must be some values more than answers changed. This suggests that the distribution is positively skewed 1 standard deviation above the mean, that is, values above 1.9 î How many standard deviations above the mean is three answers changed? 2.1 What can you say about the total number of students who changed least three answers from correct to incorrect? (Round your answer dow to the nearest whole number.) At most 1 X students changed at least three answers from correct to incorrect.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

please help, 8 and 1 isn't right for the last question.

### Analysis of Answer Changes in a Multiple-Choice Test

In a study involving 76 college students, data revealed that the average number of responses changed from correct to incorrect on a 78-item multiple-choice test was 0.9. The standard deviation was recorded at 1.0. Based on this mean and standard deviation, we aim to understand the distribution shape of the variable number of answers changed from correct to incorrect.

#### Distribution Analysis

- **Mean and Standard Deviation Interpretation:**
  - Given the mean (μ) is 0.9 and the standard deviation (σ) is 1.0, a change of 0 answers is 0.9 standard deviations below the mean (0.9 - 0.9 = 0).
  
- **Normal Distribution Assumption:**
  - If the distribution was normal, approximately 16% of students would change fewer than 0 answers. However, changing fewer than 0 answers is not logical, a hint that the distribution is not normal.
  
- **Skewness of Distribution:**
  - Values exceeding one standard deviation above the mean are those above 1.9 answers changed (0.9 + 1.0 = 1.9). Given some students change more than 1.9 answers, this indicates the distribution is positively skewed.

#### Standard Deviations From Mean

- **Calculation for Three Answers Changed:**
  - To find how many standard deviations from the mean is three answers: \((3 - 0.9) / 1.0 = 2.1\). Thus, three answers changed is 2.1 standard deviations above the mean.

#### Estimating Students Changing More Answers

- **Students Changing at Least Three Answers:**
  - Considering the data, the number of students changing at least three answers from correct to incorrect is estimated to be at most 8 (rounded down to the nearest whole number).

This analysis helps us understand student behavior regarding answer changes and the resultant distribution characteristics in academic assessments.
Transcribed Image Text:### Analysis of Answer Changes in a Multiple-Choice Test In a study involving 76 college students, data revealed that the average number of responses changed from correct to incorrect on a 78-item multiple-choice test was 0.9. The standard deviation was recorded at 1.0. Based on this mean and standard deviation, we aim to understand the distribution shape of the variable number of answers changed from correct to incorrect. #### Distribution Analysis - **Mean and Standard Deviation Interpretation:** - Given the mean (μ) is 0.9 and the standard deviation (σ) is 1.0, a change of 0 answers is 0.9 standard deviations below the mean (0.9 - 0.9 = 0). - **Normal Distribution Assumption:** - If the distribution was normal, approximately 16% of students would change fewer than 0 answers. However, changing fewer than 0 answers is not logical, a hint that the distribution is not normal. - **Skewness of Distribution:** - Values exceeding one standard deviation above the mean are those above 1.9 answers changed (0.9 + 1.0 = 1.9). Given some students change more than 1.9 answers, this indicates the distribution is positively skewed. #### Standard Deviations From Mean - **Calculation for Three Answers Changed:** - To find how many standard deviations from the mean is three answers: \((3 - 0.9) / 1.0 = 2.1\). Thus, three answers changed is 2.1 standard deviations above the mean. #### Estimating Students Changing More Answers - **Students Changing at Least Three Answers:** - Considering the data, the number of students changing at least three answers from correct to incorrect is estimated to be at most 8 (rounded down to the nearest whole number). This analysis helps us understand student behavior regarding answer changes and the resultant distribution characteristics in academic assessments.
Solution
Bartleby Expert
SEE SOLUTION
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman