1. This assignment is worth 6% of your final grade.
2. Submit your assignment electronically through eClass. Assignments submitted by email will not be accepted.
3. A list of files to submit is found at the end of this assignment. Organize your MATLAB programs as follows with your student information, the question number, and your solution in the indicated locations.
% 1570 - Winter 2021 – Assignment 4
% <Last Name>, <First Names>
% <Student Number>
% <York email address>
% Question <x> solution
clear; clc; % begin with a clean start
<put your solution here>
% *** end ***
4. To improve the readability of your MATLAB programs, ensure the statements are properly indented. This is a good habit to develop and is particularly important as your programs get more complex. Here's a quick way to get the proper indentation: (i) Open a script in the MATLAB Editor Window. (ii) Type Ctrl-A to select all the statements in the script. (iii) In the Editor ribbon, click the Smart Indent button.
1. (6 points) Write a MATLAB program (a4q1.m) to have some fun with random numbers. Begin with a banner message (see below) and then use MATLAB's randi function to initialize two integer variables: lower in the range 1 to 100, and upper in the range 101 to 1000.
Then, generate 100 random integers in the range lower to upper. Output the numbers, formatted as shown below.
As well, compute and output the following summary of the numbers:
• The lowest generated number
• The highest generated number
• The mean of the numbers
• The number of odd numbers
• The number of even numbers
• The number of prime numbers
• The prime numbers
To check for prime numbers, use MATLAB's isprime function. End with "Thank you. Bye."
Below is an example run of the program.
FUN WITH RANDOM NUMBERS
Summary
Lowest: 66
Highest: 455
Mean: 269.6
Numbers that are... odd: 51
even: 49
Number of prime numbers: 21 Primes...
311 379 173 127 277 337 379 337
251 251 127 163 373 181 149 113
233 283 193 113 443
Your program should generate output exactly as shown above, adjusted, of course, for the actual numbers generated. Output the prime numbers eight (8) per line, exactly as shown above, adjusted, of course, for the number of prime numbers. Also, output the prime numbers using a single fprintf statement and without using a loop statement.
2. (6 points) Do you work on homework with music playing in the background? Let's explore this idea. This question examines whether concentration is affected by the style of music playing in the background. A research project engaged six participants to perform a sorting task with music playing in the background. Each participant was tested on two music conditions: classical music and hip hop music. For each music condition, five sorting trials were performed. The time in seconds was recorded for each trial. Less time means faster sorting, and, arguably, better concentration. The data are shown below.
|
Participant |
Classical Music |
Hip Hop Music |
||||||||
|
1 |
2 |
3 |
4 |
5 |
1 |
2 |
3 |
4 |
5 |
|
|
1 |
54 |
44 |
48 |
42 |
42 |
53 |
51 |
47 |
42 |
40 |
|
2 |
56 |
48 |
43 |
43 |
30 |
95 |
53 |
55 |
60 |
49 |
|
3 |
62 |
58 |
54 |
47 |
41 |
84 |
89 |
85 |
64 |
63 |
|
4 |
46 |
42 |
34 |
29 |
28 |
48 |
41 |
41 |
33 |
33 |
|
5 |
72 |
44 |
43 |
37 |
43 |
79 |
50 |
40 |
38 |
32 |
|
6 |
63 |
59 |
42 |
40 |
41 |
78 |
58 |
70 |
55 |
57 |
The data are stored in the file sorting_task.txt which is available on eClass with this assignment. Write a MATLAB script (a4q2.m) that reads the data into a matrix ST. Do not output the data. Analyse the data to determine
• the mean sorting time in seconds over all trials in the experiment,
• the mean sorting time for each music condition (classical vs. hip hop),
• which music condition took less time in the sorting task and by what percentage relative to the other condition, and
• whether the difference in sorting time between the two music conditions was statistically significant.
Your MATLAB script should output the results of the above analysis in the command window. The output should look like this:
=========================================================
Effect of Background Music on Concentration (using a sorting task)
Result for sorting time Grand mean: xxxxx (s)
Results by listening condition Classical music: xxxxx (s)
Hip hop music: xxxxx (s)
Summary
Sorting time was xxxx% less while listening to xxxx music Significance test: t(xxx) = xxxxx, p = xxxxxx (xxx)
Insert values in the output where you see x's above. The values should be computed from the data. Do not type the values into your script. The first three values are times in seconds (with two decimal places). The next computed value is the difference as a percent (with one decimal place) for the music condition that took less time in the sorting task relative to the condition that took more time. On the same line, the next computed value is either "classical" or "hip hop"; i.e., the music condition that took less time overall in the sorting task.
The final line of output text gives the results of a t-test to determine if the difference in sorting time between the two music conditions was statistically significant. The four computed values, in order, are
• the degrees of freedom (an integer)
• the t-statistic (with two decimal places)
• the probability (with four decimal places), and
• either "significant" (if p < .05) or "not significant" (if p ≥ .05)
For the significance test, review example 2 in lecture 7 (Statistical Functions). There is one minor difference here. You need to use the function ttest, rather than ttest2, which was used in example 2 in lecture 7.1
3. (4 points) An experiment with 16 participants was conducted to compare four soft keyboards for text entry on smart phones. For each keyboard, nine trials were administered. Each trial involved entering a phrase of text. The text entry speed in words per minutes (wpm) was logged for each trial. The following data were collected. Each value is the mean text entry speed (wpm), averaged over 16 participants for the corresponding trial.
|
Trial |
Qwerty |
Octopus |
TP_Curve |
TP_Plus |
|
T1 |
53.34 |
24.65 |
28.69 |
26.91 |
|
T2 |
50.89 |
34.99 |
31.31 |
30.24 |
|
T3 |
52.29 |
47.55 |
31.27 |
35.74 |
|
T4 |
52.04 |
54.73 |
32.35 |
36.89 |
|
T5 |
57.71 |
61.59 |
36.31 |
40.92 |
|
T6 |
56.64 |
66.84 |
36.47 |
41.83 |
|
T7 |
54.87 |
62.52 |
40.09 |
44.12 |
|
T8 |
52.57 |
68.90 |
41.15 |
44.98 |
|
T9 |
55.47 |
70.83 |
40.30 |
46.27 |
The above data are in the file keyboard_comparison.txt which is available in eClass with this assignment. Additional details on the data are found in keyboard_comparison_readme.txt, also available on eClass.
Write a MATLAB program (a4q3.m) that uses the readtable function to read the data from keyboard_comparison.txt into a table T. Process the data to compute the mean and standard deviation of the entry speed over the nine trials for each keyboard. Generate output to the Command Window, formatted as follows
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