Applied Statistics 161.111
Assignment 1
Due date: 11PM Wednesday 23 August 2023 (NZST)
Total marks: 30Assessment value: 17%
The population we are considering for this assignment are the 135,000 kuku (New Zealand green–lipped mussels) growing in a mussel farm spread over 2 sites in the Marlborough Sounds.
The file (Mussels- yes';font-family:'Arial Unicode MS';mso-fareast-font-family:MicrosoftYaHei;
line-height:114%;color:rgb(0,0,0);font-size:9.0000pt;" >) contains data from a sample of 294 mussels. This includes, for each mussel, its length (measured in mm), its grade (classified as large, medium or small) and the site it was grown (site A or site B).
• Use the sample data to answer the following questions in the spaces provided. You can re-size the answer spaces.
• Use Excel and incorporate the output into your answers.
Part A: Exploratory analysis on categorical data (Grade of Kuku) [8 marks]
1. Use Excel to produce a table of counts for the different grades of kuku in the sample. [2 marks]
2. Use Excel to draw an appropriate graph to display the table you created above. Label graphappropriately. [2marks]
3. What does the graph and table tell you about grades of kuku in the sample? [2 marks]
4. The sample was selected using stratified random sampling, where the kuku grades were used as the strata. Use this to estimate the number of mussels of each grade in the Marlborough Sounds mussel farm. Are these figures exact? Explain. [2 marks]
Part B: Exploratory analysis on numerical data (Length of Kuku) [10 marks]
1. Use Excel to draw a boxplot of the lengths of kuku in the sample.Label graph appropriately. [2 marks]
2. Use Excel to draw a histogram of the lengths of kuku in the sample.Label graph appropriately. [2 marks]
3. Use Excel to calculate the numerical summaries of the lengths of kuku in the sample. Fill in the table with the values rounded to 1 decimal place.[2 marks]
| Kuku Lengths (mm) |
Mean | |
Standard deviation | |
Minimum | |
Lower Quartile | |
Median | |
Upper Quartile | |
Maximum | |
4. What do your plots and summary statistics tell you about lengths of kuku in the sample? Consider centre, spread, shape and outliers.[4 marks]
Part C: Confidence interval for the mean [12 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: [4 marks]
Standard error = Confidence interval: Lower limit = Upper limit = |
2. Write a sentence to interpret your confidence interval in context.[4 marks]
3. Are the conditions for this confidence interval met? Explain. [2 marks]
4. Before the data was collected the manager of the Marlborough Sounds mussel farm claimed that the average length of the kuku on their farm is greater than 100mm. Does your confidence interval support the manager’s claim? Explain.[2 marks]
