Assignment 2 - Shubh Chand (FB)
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BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Assignment 2 Worksheet Questions
Complete all of the questions
highlighted in yellow on this Worksheet, then
transfer your
answers to the questions provided in the Assignment Submission Dropbox
by the deadline
of Monday, October 30, 2023 (by 11:59 p.m.).
Name: Shubh Chand Student ID: 100864070
Answer all of the highlighted questions on this Worksheet in the space provided. There are 25
questions. Keep your answers brief and concise. PART A: Questions on EXPERIMENTAL DESIGN
Question 1: Give one
suitable question
for this study based on the information provided in the study scenario.
Do the colours of flowers determine which flowers the hummingbird prefers?
Question 2:
State a
research hypothesis
that can be tested in a study of hummingbird feeding behaviour.
Express the research hypothesis in your own words
.
If two species of hummingbirds engage in nectar competition across various flowers, then it is hypothesized that by observing their feeding patterns over a specific duration, we can ascertain which flower colour is predominantly visited by each hummingbird species.
Question 3:
State the prediction
that follows from the research hypothesis suggesting a design for a study to test the hypothesis. Use an "
If
…. then
…" statement.
Express your answer in your own words
and keep the answer brief (less than 50 words). If we hypothesize that hummingbirds may exhibit a preference for certain flower colours,
then an experiment could involve situating an equal quantity of flowers of various colours near controlled hummingbird feeding areas. This setup would allow us to monitor which flowers are most frequently visited and by which hummingbird species.
Question 4:
When deciding on the most appropriate statistical test to be used for data analysis, what is the main distinction
between using the Chi-square Test or using the Student’s t
Test.
Answer this question in your own words.
(Be concise using less than 50 words).
The distinction between the Chi-Square test and the Student's t-test lies in their respective approaches to data analysis. The Chi-Square test evaluates the variance between expected values and observed values in the data by employing a predefined model, while the Student's t-test assesses the 1
BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis probability of differences between sample groups being statistically significant by considering the mean and standard deviation.
PART B: Chi-square Analysis There are two problems
requiring the use of the Chi-square Test:
−
Problem 1 - analyzes data from a field study on the flower colour preferences of the Rufous Hummingbird population near Kelowna, B.C. (August 2022)
−
Problem 2
- analyzes data from a field study on the flower colour preferences of the Calliope Hummingbird population near Kelowna, B.C. (August 2022)
Question 5: State the
Null Hypothesis (Ho) for a Chi-square Test for Problems 1 and 2.
The color preference for Rufous hummingbirds is unlikely to be influenced by the abundance of nectar in their environment.
Question 6: State the Alternative Hypothesis (H
A
) for a Chi-square Test for Problems 1 and 2. An environment with an abundance of nectar is expected to influence the color preference of hummingbirds.
PROBLEM
1 – A Study of Feeding Behaviour by Rufous Hummingbirds Results: The data from the Kelowna Study of the number of flower visits by Rufous hummingbirds to a variety of flower colours were collected and summarized in Table 1 below. These data will be analyzed using the Chi-square Test in Problem 1 on this Worksheet. The Chi-square Test analysis is summarized in Table 2
.
Table 1. Average number of visits by Rufous hummingbirds to flowers of various colours over a one-hour observation period at the Kelowna B.C. field study site in August 2022. Average of 10 observation periods.
Table 2. Chi-Square analysis of behaviour of Rufous hummingbirds at the Kelowna B.C. field study site. 2
Colour of Flower
Blue
Orange
Purple
Red
Yellow
Number of times that Rufous Hummingbirds visited flowers over a 1 hour period of study
64
78
48
89
71
BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis CATEGORIES
(description of Flower Colour)
OBSERVED
NUMBER OF
VISITS / HOUR
(from Table 1)
EXPECTED
NUMBER OF
VISITS / HOUR
(= based on Ho)
CHI-SQUARE VALUE
(Obs.-Exp.)
2
Expected
Purple Flowers
48
64
4
Blue Flowers
64
64
0
Yellow Flowers
71
64
0.77
Orange Flowers
78
64
3.063
Red Flowers
89
64
9.766
TOTAL
320
320
17.599
For your data analysis, refer to Week 4-Lecture 8
and the other posted resources to find the steps that are to be followed to calculate the Chi-Square Value
for each flower colour and the total Chi-
square value as well as to determine the degrees of freedom (df) for the data in Table 2. Question 7: Use the Chi-Square Analysis Table
(
Table 2
in this Assignment 2 Worksheet
)
and the Table of Critical Chi-square Values (
Table A from Assignment 2 folder entitled “Resources for Statistical Analyses”
)
to determine the
answers to the following questions. (a) The number of categories (n)
(with no decimal places
)
involved is 5
(b) The degrees of freedom (df)
(with no decimal places)
are 4
(c) The calculated Chi-Square value
(to 2 decimal places)
that was obtained in Table 2 (above) is 17.60
(d) The critical Chi-Square value
(to 2 decimal places)
that was obtained from Table A
(posted in Assignment 2 Resources folder) is 11.07
Question 8: What is your Conclusion from the Chi-square Test
analysis after comparing your calculated Chi-square value (Table 2 above) and the Critical Chi-square value (Table A provided with the Assignment 2 Instructions and Worksheet
)? Choose one answer
.
A.
fail to reject the null hypothesis (Ho)
B.
reject the null hypothesis (Ho)
3
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BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Question 9: Briefly explain your answer to Question 8 (do not exceed 50 words).
According to the data, the Chi-Square value that was calculated was 17.60 which is greater than the critical Chi-Square Value and which therefore rejects the null Hypothesis. Question 10: State your
conclusion to your statistical analysis and relate it back to your Research Hypothesis
. Use the format for reporting statistical results given in Week 6-
Lecture 12
on writing the text for a results section. Answer this question in your own words. Keep your answer brief (do not exceed 100 words).
Rufous’s Hummingbirds successfully showed that red was the most frequented colour visited within one hour. Problem 2 – A Study of Feeding Behaviour by Calliope Hummingbirds
Results: The data from the study of the number of flower visits by Calliope hummingbirds to a variety of flower colours were collected and summarized in Table 3
below; these data will be analyzed using the Chi-square Test in Problem 2 on this Worksheet. The Chi-square Test analysis is summarized in Table 4.
Table 3. Average number of visits by Calliope hummingbirds to flowers of various colours over a one-hour observation period at the Kelowna B.C. field study site in August 2022. Average of 10 observation periods.
Colour of Flower
Blue
Orange
Purple
Red
Green
White
Yellow
Number of times hummingbirds visited flowers over a 1 hour period of study
71
89
73
96
68
81
82
Table 4. Chi-Square analysis of behaviour of Calliope hummingbirds at the Kelowna B.C. field study site. CATEGORIES
(description of Flower Colour)
OBSERVED
NUMBER OF
VISITS
(from Table 1)
EXPECTED
NUMBER OF
VISITS
(= based on Ho)
CHI-SQUARE VALUE
(Obs.-Exp.)
2
Expected
Blue Flowers
71
80
1.0125 Orange Flowers
89
80
1.0125
Purple Flowers
73
80
0.6125
Red Flowers
96
80
3.2
Green Flowers
68
80
1.8
4
BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis White Flowers
81
80
0.0125
Yellow Flowers
82
80
0.05
TOTAL
560
560
7.7
For your data analysis, refer to Week 4-Lecture 8 and the other posted resources to find the steps that must be followed to calculate the Chi-Square Value
for each flower colour and the total Chi-
square value as well as to determine the degrees of freedom (df) for the data in Table 4. Question 11: Use the Chi-Square Analysis Table
(
Table 4
in this Assignment 2 Worksheet
)
and the Table
of Critical Chi-square Values (
Table A from Assignment 2 folder entitled “Resources for Statistical Analyses”
)
to determine the
answers to the following questions. (a) The number of categories (n)
(with no decimal places)
involved is 7
(b) The degrees of freedom (df)
(with no decimal places)
are 6
(c) The calculated Chi-Square value
(to 2 decimal places)
that was obtained in Table 4 (above) is 7.7
(d) The critical Chi-Square value
(to 2 decimal places)
that was obtained from Table A
(posted in Assignment 2 Resources folder) is 12.692
Question 12: What is your Conclusion from the Chi-square Test analysis
after comparing your calculated Chi-square value (from Table 2 above) and the Critical Chi-square value (from Table A provided with the Assignment 2 Instructions and Worksheet)? Choose one answer.
A.
fail to reject the null hypothesis (Ho)
B.
reject the null hypothesis (Ho)
Question 13: Briefly explain your answer to Question 12 (do not exceed 50 words).
The calculated Chi-Square value is 7.7 and the critical Chi-Square value is 12.692, the calculated is lower than the critical therefore we fail to reject the null hypothesis. Question 14: State your
conclusion to your statistical analysis and relate it back to your Research
5
BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Hypothesis
. Use the format for reporting statistical results given in Week 6-Lecture 11
on writing the text for a results section. (
Answer this question in your own words. Keep your answer brief - do not exceed 100 words).
PART C: Student’s t
Test Background Information:
After completing the observational study on the feeding behaviour of hummingbirds based on the number of visits the hummingbirds made to flowers of different colours, it was possible to draw some conclusions about colour preferences (Problems 1 and 2 in PART B) and generate more questions. For PART C
, a second aspect of feeding behaviour in hummingbirds was examined by measuring the amount of time (in sec) that 35 individuals
of each hummingbird species spent feeding at red flowers over a 12-hour period. Thirty-five individual birds of each species were tagged and then monitored for their feeding behaviour at red flowers. The time spent (in seconds) by each bird at 10 different red flowers over a 12-hour period was measured and averaged. These average values were then entered
in the data table (Table 5) provided below for each bird that was monitored. Experimental Design of Study of Feeding Times:
– fill in the steps of the study below
Question 15:
Give one suitable question
for this comparison study (described in Problem 3)
based on the information provided in the study scenario.
Question 16:
State a
research hypothesis
(in Problem 3)
that can be tested in a study of hummingbird feeding behaviour.
Express the research hypothesis in
your own words
and keep answer brief (less than 50 words)
.
6
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BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Question 17:
State the prediction
that follows from the research hypothesis
(for Problem 3) suggesting a design for a study to test the hypothesis. Use an "
If
…. then
…" statement.
Express your answer in your own words and keep answer brief (less than 50 words). There is one problem
requiring the use of the Student’s t Test:
Problem 3 - analyzes data from a field study on the feeding times at red flowers by two species of hummingbirds at a study site near Kelowna B.C. in the summer of 2022.
Question 18: State the
Null Hypothesis (Ho) for this Student’s t
Test analysis Question 19: State the Alternative Hypothesis (H
A
) for this Student’s t
Test analysis Problem 3 – A Comparative Study of Visiting Times to Red Flowers by Two Species of Hummingbirds
Student’s t Test Analysis for Problem 3
– fill in each of the steps for data analysis below
Results: data were collected and summarized in Table 5 below
; these data will be analyzed using the Student’s t
test
A survey was conducted on two hummingbird species that are found together at a field study site in Kelowna B.C. The average amount of time (in seconds) that each of 35 individual hummingbirds from each of the two species spent feeding at 10 individual red flowers over a 12-hour period in August 7
BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis 2022 was recorded. These data require a Student’s t
Test for a statistical analysis of the feeding behaviour based on the length of time spent feeding. To save time entering these data into Excel and to avoid making any data entry errors, you can copy and paste this data table (Table 5) directly into Excel and then complete the necessary calculations to complete Table 6. Table 5. Average time (in seconds) spent feeding at 10 different red flowers at the Kelowna Study Site by 35 individual Rufous hummingbirds and 35 individual Calliope hummingbirds over a 12-hour period in August 2022.
Sample
Average time (in sec) spent feeding on individual red flowers
Bird #
Rufous Hummingbirds
Calliope Hummingbirds
1
43
51
2
37
48
S 54
44
4
40
46
5
49
52
6
43
48
7
42
65
8
42
45
9
46
64
10
34
45
11
42
44
12
35
53
13
66
49
14
35
43
15
33
33
16
35
43
17
44
34
18
33
55
19
45
53
20
38
44
8
BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis 21
64
47
22
55
46
23
38
65
24
46
38
25
52
57
26
60
47
27
54
43
28
59
52
29
58
43
30
46
56
31
26
43
32
32
49
33
31
47
34 43
38
35
25
42
For your data analysis, refer to the posted resources to find the steps that must be followed to calculate the sample t
statistic and determine the degrees of freedom (df) for the data in Table 5. Use Table 6
to calculate the detailed information required for the Student’s t Test analysis. Table 6. Summary of the Student’s
t
Test analysis of the feeding times of two hummingbird species at red flowers using Excel.
Student’s t
-Test: Two-Sample Assuming Equal Variances
Variable 1
Variable 2
Rufous
hummingbirds
Calliope
hummingbirds
Mean
(use two decimal places)
Variance
(use two decimal places)
Standard Deviation (SD)
(use two decimal places)
Number of Observations or Sample Size
(n)
(use no decimal places)
Degrees of Freedom (df)
(use no decimal places)
Calculated t
Statistic
(use three decimal places)
Critical t
Critical two-tail
(use three decimal places)
Probability
(
p
)
two-tail
(use three decimal places)
Probability Cut-off (
p
) (use two decimal places)
9
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BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Question 20: From the
Student’s t
Test analysis (in Table 6), summarize the basic descriptive statistics for the Rufous hummingbird population studied at Kelowna B.C. (a) The overall mean feeding time (in sec) at red flowers for 35 Rufous hummingbirds is (use 1 decimal place) (b) The standard deviation
for the Rufous hummingbirds is (use 1 decimal place) Question 21: From the
Student’s t
Test analysis (in Table 6), summarize the basic descriptive statistics for the Calliope hummingbird population studied at Kelowna B.C. (a) The overall mean feeding time (in sec)
at red flowers for 35 Calliope hummingbirds is (use 1 decimal place) (b) The standard deviation
for the Calliope hummingbirds is (use 1 decimal place) Question 22: Use the summary of the Student’s t
Test analysis (
provided in Table 6 above) and the Critical t
Values (provided in Table B) to determine the p
-value and
interpret the results of this analysis.
(a) The total sample size (n)
(with no decimal places)
for both species combined is (b) The degrees of freedom (df)
(with no decimal places)
are (c) The Calculated t
Value
(from Table 6) (with 3 decimal places)
is (d) The Critical t
Value (at p
=0.05) from the Critical t
Table
(Table B in Assignment 2 Resources folder)
(with 3 decimal places)
is (e) The probability (
p
value)
from calculations in Excel (with 2 decimal places)
is Question 23: What is your Conclusion from the Student’s t
Test analysis
after comparing your calculated t
-value (from Table 6 above) and the Critical t
-value (from Table B provided with the Assignment 2 Instructions and Worksheet)? Choose one answer.
A.
fail to reject the null hypothesis (Ho)
B.
reject the null hypothesis (Ho)
10
BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Question 24: Briefly explain your answer to Question 23 (do not exceed 50 words)
. Question 25: State your
conclusion to your statistical analysis and relate it back to your Research
Hypothesis
. Use the format for reporting statistical results given in Week 6-Lecture 11
on writing the text for a results section. (
Answer this question in your own words. Keep your answer brief - do not exceed 100 words).
11
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