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Applied Statistics
创建日期：2024-08-19 14:51:26
所属分类：统计学statistics
标签： Statistics
Applied Statistics

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Applied Statistics


Assignment 2 Solutions

Total marks:  45 Assessment value: 17%

Background

This assignment uses the same dataset as Assignment 1. The population of interest is round cut diamonds for sale in New Zealand.

Data was collected from a random sample of 229 round cut diamonds from a single New Zealand based retailer of diamond jewellery.

The data consists of the price of the diamond (in $NZ), the colour grade (a six point scale from D to I, D being colourless to I being nearly colourless) and the Lab which did the certification of the colour grade (Lab A or B). The data is in the Excel file Diamonds_2024_S1.xlsx

Import this data into RStudio and call it diamonds.

Use the data to answer the following questions in the spaces provided.  You can re-size the answer spaces.

Use RStudio and incorporate the code you used and the output into your answers. 

When you are finished your assignment, save it as a pdf and upload to Stream Assignment 2 Dropbox.

Part A: Comparing means: Analysis of diamond price according to lab of certification [25 marks]

We are interested in whether the average price of round cut diamonds differs depending on the lab that did the certification.

A1: Use RStudio to draw a side-by-side boxplot of price versus lab for the diamonds in the sample. Include your code as well as your plot.   [3 marks] 

A2: Use RStudio to calculate numerical summaries for price for each lab. Fill in the table with the values rounded appropriately.  Include your code below the table. [4 marks] 

 

Lab A

Lab B

Minimum

 

 

Lower Quartile

 

 

Median

 

 

Mean

 

 

Upper Quartile

 

 

Maximum

 

 

Sample size

 

 

Rcode used:

A3: What do the plots and numerical summaries tell you about the prices of diamonds that were classified by the different labs in the sample? Hint: consider comparisons of centre, spread, shape and outliers.  [4 marks]

A4: Do a two-sample t-test to determine if there is any evidence that there is a difference in mean prices for diamonds certified by Labs A and B in the population. 

a. Step 1: Write the hypotheses. [2 marks]

  The null:

  The alternative:

b. Use RStudio to do the two-sample t-test. Include your code and output. [1 mark] 

c. Step 2: State the value of the test statistic. [1 mark]

d. Step 3: State the statistical decision with reason. [1 mark] 

e. Step 4: Write your conclusion.   [2 marks] 

f. Step 5: Check the conditions are met. [1 mark]

The issue of lack of representativeness was discussed in Assignment 1. Discuss whether the normality condition is met.    

g. Write a sentence to interpret the confidence interval. Explain how it adds to your conclusion. [4 marks]

A5: Explain why a two-sample t-test is better than a t-test of differences for this context.  [1 mark]

A6: An employee noted that Lab A tends to certify diamonds that are more expensive. She picks two diamonds from the store’s catalogue and looks up which lab certified which diamond. However, she sees that the more expensive diamond was certified by lab B.  Does this contradict the analysis in A4? Explain. [1 mark]

Part B: Exploratory Data Analysis of Lab and Colour Grade.  [9 marks]

We are interested in investigating if the distribution of the colour grade depends on which lab certified the diamond.

B1: Use RStudio to produce a table of counts for the colour grade of the diamonds by the Lab that certified them. Put lab as the rows and colour as the columns. Include your code and table.     [2 marks]

B2: Use RStudio to produce a table of diamond colour grade as a proportion of the total number of diamonds certified by each lab. Round the values to 2 decimal places.  Include your code and table. Note: the rows of your table should sum to 1. [2 marks]

B3: Use RStudio to produce a side-by-side bar plot of the distribution of diamond colour grade as a proportion of the diamonds certified by each lab. Include your code and plot. [2 marks]

B4: What do the tables and plot tell you about the distribution of colour grade for the two labs? [3 marks] 

Part C: Inferential Analysis of lab and colour.  [11 marks]

C1: Do a Chi-squared test of lab and colour.

a. Step 1: Write the hypotheses. [2 marks]

  The null:

  The alternative:

b. Use RStudio to do the Chi-Squared test. Include the RStudio output here. Include your code and output. [1 mark]

c. Step 2: State the value of the test statistic.   [1 mark]

d. Step 3: State the statistical decision with reason. [1 mark] 

e. Step 4: Write your conclusion. [1 mark] 

f. Step 5: Check the conditions are met. [2 marks]

The issue of lack of representativeness was discussed in Assignment 1. What is the other condition? Discuss whether this condition is met.    Include any code you use and its output. 

g.  Use RStudio to calculate the residuals. Include your code and output [1 mark] 

h. Do the residuals add to your conclusion? Explain. [2 marks]

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EMESTER1 MAS8383 ECO 512 STAT 8310 CMN3102 MA577 CMPT 225 COMP0045 Methods Equations MATH 113 Math 3283W ICS-33 EN4302/ENT603 BIA B350F MA318 MTHM506 MECH 5315M ECONOMICS MAS8382 COM 2004 PX3142 XJEL 3662 STAT 231 MGT B399F PX4131 COM2108 30AM MSCI521 ECONM1015 ACFI304 GR5241 MATH10101 ECON 2070 COMS31900 EFIM20011 CSE 250B ACSE-5 STAT4207 SOFT2412 ELEC 331 AY2020 MSIN0209 FIT2094 CS 241L ST404 CS 411 3D CA3 INF4002 COMP3506 SIT718 CS 188 CS 170 MATH 138 CSE 251A CMT118 DATA5207 CMPT307 CMPT459 T1 PGEE11108 COSC 3P32 ME 163 MATH96007 7QQMM203 EE6227 BA 574 STA 4234 ECO206Y1Y ECO2008 MT2300 MATH 11158 CS 527 MACM 316 CSE474 2DI70 ISE 525 COMP3411 EMAT30007 7CCSMBDT MFIN704 MFIN704W21 MfIB ECE 438 CS 436 F36 CS5344 FE 621A FE621 TBA 612 ECM3151 ECMM422 MF1 MSIN0107 ESSMENT CS 5854 MFIT 5008 MIPS R4000 ENG5274 BU52018 ENG2079 BIOA02 STA2570 F0 INF553 STAT 440 STAT3008 COMP9417 COMP6451 6COM1042 BU52006 ST303 HW-1 CISC-235 CS 510 MATH3161 ECN 140 ECE391 Comp 3613 CVEN 9625 PRG455 UESTION 1 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