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Name: _______Uguz Ghany ______________ ID number: ______16203548 ___________
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Applied Statistics 161.111
Assignment 1
Due date: Friday 24 April 2020
Total marks: 50
The population data
The population we are considering for this assignment are the 10,000 kuku (New Zealand green–lipped mussels) growing in a mussel farm in the Marlborough Sounds. The variables of interest are the length of the kuku (in millimetres), grade (small, medium or large) and sex (male or female).
Each kuku (mussel) has a unique ID. The population consists of:
· 1948 large kuku with ID numbers from 1 to 1948.
· 4457 medium kuku with ID numbers from 1949 to 6405
· 3595 small kuku with ID numbers from 6406 to 10000.
You do not have access to the population data. You will collect a sample using the following steps.
· Click on the following link to open a Shiny app in your web-browser and type your ID number into the “Student ID:” box.
· http://shiny.massey+.ac.nz/dleader/DataDownload111/
· This will generate an Excel file containing ID, length, grade and sex for each of the kuku in your sample. This is your sample data. The file you have downloaded is unique to you.
· Keep an electronic copy of your sample data for use in Assignment 2.
· Attach a copy of your sample data to the appendix.
· Use your sample data to answer the following questions in the spaces provided. You can re-size the answer spaces.
· Use Excel and incorporate the Excel output into your answers in the document below.
Part A: The Sampling Method [11 marks]
1. Your sample has been generated using the stratified random sampling method, where the kuku grades were used as the strata. Describe the process behind taking the sample with enough detail that someone could use your description to collect a sample them self. [7 marks]
The Stratified Random Sampling is a sampling method that involves dividing the population into small sub-group known as strata. These small groups called strata are formed based on the attribute or characteristics that are shared among the members under the study.
After dividing the population into strata, random samples are selected from the strata, which will be used during the study.
For example, let the population consist of total Number of Kuku; the kuku population is divided into K-units with the ith stratum that consists of Kuku units. After the stratum has been selected, a sample size of n Kuku from the ith stratum is then selected, which will be used for the study.
Talk about the actual Stratified sampling method for the Kuku, not Ni or what ever you talked about in the second paragraph.
2. Why is stratified random sampling an appropriate method to use with this population? [3 marks]
The method is appropriate since the sample being studied has a minimal variance, and the objective of the study is to estimate the population parameters that have the highest precision. Also, the method is appropriate since the population consists of two clear groups. This ensures that both groups are clearly represented.
3. Paste a copy of your data in the appendix. [1 mark]
Part B: Exploratory analysis on categorical data [9 marks]
1. Use Excel to produce a table of counts for the sex of the kuku in your sample. [2 marks]
Sex of kuku table of counts
Male
53
Female
47
Totals
100
2. What proportion of your sample are female kuku? [2 marks]
Total Female Kuku was 47 of a total Kuku amount of 100. Thus, the proportion will be
47/100
3. Use Excel to draw an appropriate graph to display the table you created above. [4 marks]
4. What does your graph tell you? [1 mark]
From the Graph, we Can observe that there is more Kuku male compared to Kuku female.
We can note from the graph that generally, male kuku are longer than female kuku.
As there is only 2 units to observe (male and female Kuku) we cannot draw on the centre, spread, shape, or if there are any outliers.
Part C: Exploratory analysis on numerical data [15 marks]
1. Use Excel to draw a boxplot of kuku lengths. [3 marks]
2. Use Excel to draw a histogram of kuku lengths. [4 marks]
Paste your graph here
3. Use Excel to calculate the numerical summaries of the kuku lengths. Fill in the table with the values rounded to 2 decimal places. [4 marks]
Kuku Lengths
Sample size
100
Mean
100.41
Standard deviation
47.62
Minimum
11.9
Lower Quartile
66.95
Median
92.3
Upper Quartile
122.55
Maximum
234.8
4. What do your plots and summary statistics tell you about kuku lengths in your sample? Consider the centre, spread, shape and outliers. [4 marks]
The lengths of the Kuku are cantered at the mode of the length where most of the length is distributed at 92.3mm length.
The range is 222.9mm thus tells us the lengths are highly spread.
The graph of the lengths is positively skewed with one peak where most of the length is concentrated at left (35mm).
There are three outliers 234.8mm, 216.1mm, and 212.7mm that were identified in the Kuku length.
Part D: Confidence interval for the mean [15 marks]
1. Calculate a 95% confidence interval for the mean length of kuku on the Marlborough Sounds mussel farm. To get full marks you must show your working for the following: [7 marks]
Standard error = Standard Deviation/ Sqrt of Counts
=47.62 /√100
SE = 4.762 mm
Confidence interval = using the Excel you can find confidence interval
= 9.45
Lower limit = calculated by subtracting confidence interval from the mean of the length
= 100.41 – 4.765 x 2
= 90.886 mm
Upper limit = calculated by adding the mean and the confidence interval
= 100.41 + 4.765 x 2
= 109.934 mm
95% confidence interval is between 90.886 mm and 109.934 mm.
2. Write a sentence to interpret your confidence interval in context. [4 marks]
We are 95% certain that the interval from 90.96 to 109.86 captures the true mean lengths of Kuku on the Marlborough Sounds mussel farm.
3. Are the conditions for this confidence interval met? Explain. [2 marks]
Yes, the conditions are met.
This is because the samples used during the study was stratified random sampling method.
Also, the sample size of kuku is larger than 30, hence the sampling distribution is normal.
4. Before the data was collected the manager of the mussel farm claimed that the average length of the kuku on the farm is 100mm. Does your confidence interval support the manager’s claim? Explain. [2 marks]
Yes, the confidence interval supports the manager’s claims since the mean lies between the lower and upper limit of the confidence interval, and thus the manger was correct about the claim.
+ + + + + + + +
Appendix:
Paste your data here: [1 mark]
ID
Length
Grade
Sex
496
216.1
Large
Female
883
169.9
Large
Male
546
217.8
Large
Male
843
202.2
Large
Male
1483
178.5
Large
Female
54
173.7
Large
Male
281
155
Large
Female
379
150.9
Large
Female
563
179
Large
Female
582
158.9
Large
Male
1660
129.2
Large
Male
1311
197.6
Large
Female
788
212.7
Large
Female
995
234.8
Large
Female
905
179.9
Large
Male
1312
187.7
Large
Male
1652
152.5
Large
Female
1032
173.2
Large
Male
250
148.3
Large
Male
4466
82.4
Medium
Female
3556
93.8
Medium
Female
2316
98
Medium
Female
5546
96.6
Medium
Female
5567
111.6
Medium
Female
4859
91
Medium
Male
5187
80.9
Medium
Male
5071
92.3
Medium
Male
5077
101.1
Medium
Female
4984
88
Medium
Male
2322
82.3
Medium
Male
4043
121
Medium
Female
3983
107.8
Medium
Male
3312
117.3
Medium
Female
5684
122.1
Medium
Male
4605
105.1
Medium
Female
2243
79.6
Medium
Male
2617
129.7
Medium
Female
3030
105.1
Medium
Male
3431
128
Medium
Male
2410
118.2
Medium
Female
5198
105.3
Medium
Male
6356
63
Medium
Male
4499
107.8
Medium
Female
2982
82
Medium
Male
4885
77.7
Medium
Female
3418
94.1
Medium
Female
2200
116.9
Medium
Male
2382
129.3
Medium
Male
6346
67.4
Medium
Male
2830
104
Medium
Male
5661
96.2
Medium
Female
5480
91.6
Medium
Male
5125
92.3
Medium
Female
2986
122.7
Medium
Female
6374
72.8
Medium
Female
5449
98.4
Medium
Female
2224
93.9
Medium
Male
3264
75.4
Medium
Male
5021
133.4
Medium
Male
5869
85.2
Medium
Female
2715
135.8
Medium
Male
3706
113.9
Medium
Male
4450
101.6
Medium
Female
5085
100.7
Medium
Female
7731
48.7
Small
Female
6929
89.9
Small
Male
7785
74.2
Small
Male
8572
47.9
Small
Female
8120
59.1
Small
Female
7551
68.9
Small
Male
6480
83.8
Small
Female
9417
63.9
Small
Male
9081
49.1
Small
Male
8507
61.1
Small
Male
7406
49.2
Small
Female
8694
70.7
Small
Female
7982
37.6
Small
Female
8003
12.6
Small
Female
8006
52.8
Small
Female
7734
58.1
Small
Male
7687
11.9
Small
Male
8553
72.3
Small
Male
7770
67.6
Small
Male
9740
35.2
Small
Male
8013
62.8
Small
Male
7728
50.1
Small
Female
8552
74.3
Small
Female
9404
66.8
Small
Female
8711
50.6
Small
Female
7314
33.4
Small
Male
8042
51.3
Small
Male
9379
43
Small
Male
8815
70.4
Small
Male
9844
61
Small
Female
6953
100.2
Small
Female
6421
87.7
Small
Male
8660
47
Small
Male
6534
78.5
Small
Male
9290
54.7
Small
Male
8135
63.4
Small
Female
Bar Chart for Count
Male Female 53 47
Assignment 1 Page 1
