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Name: _______Uguz Ghany ______________ ID number: ______16203548 ___________

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