Lamb birth weight is the single largest influence on survival of lambs in the first few days of life. In a trial at Massey University in the late 1990s, 160 mixed-aged, Coopworth pregnant ewes (female sheep) were randomly allocated to an experiment involving two shearing treatments (shorn on day 70 vs not shorn) and four feeding regimes (HH, HM, MH, MM). The first letter refers to feed during days 70-101 of pregnancy, and the second during days 102-140. The M (maintenance) feeding group were fed at a level calculated to maintain maternal conceptus-free weight, while the H (high) feeding group were fed to gain around 100g per day above this during the relevant period.

After each lamb was born, its birthweight was recorded, as well as its rank (whether it was a single or twin).

The data are in the Excel file lambs.xlsx.

Use the 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 of the feeding regimes [10 marks]

A1: Use Excel to produce a table of counts for the different feeding regimes. [2 marks]

A2: Use Excel to draw an appropriate graph to display the table you created above. [2 marks]

A3: What does the graph and table tell you about the numbers of lambs from ewes in the different feeding regimes? Does it suggest that the feeding regime affects the number of lambs born to a ewe? [2 marks]

A4: Why are there not equal numbers of lambs in each feeding regime? What does this tell you about the allocation of ewes to the different feeding groups? Explain. [2 marks]

A5: Explain why the random allocation of ewes to the different feeding regimes is an important part of the experimental design. How does this random allocation affect the conclusions? [2 marks]

Part B: Exploratory analysis of birthweight [10 marks]

B1: Use Excel to draw a boxplot of birthweight for all the lambs. [2 marks]

B2: Use Excel to draw a histogram of birthweight for all the lambs. [2 marks]

B3: Use Excel to calculate the numerical summaries of birthweights of the lambs. Fill in the table with the values rounded sensibly. [2 marks]

Weight (kg)

Mean

Standard deviation

Minimum

Lower Quartile

Median

Upper Quartile

Maximum

B4: What do your plots and summary statistics tell you about birthweights of the lambs? Write one or two sentences about each of the following: centre, spread, shape and outliers. [4 marks]

Part C: Confidence interval for mean birthweight [12 marks]

C1: Calculate a 95% confidence interval for the mean birthweight of Coopworth lambs in the population. To get full marks you must show your working for the following: [4 marks]

Standard error =

Confidence interval =

Lower limit =

Upper limit =

C2: Write a sentence to interpret your confidence interval in context. [2 marks]

C3: Two conditions (normality and representativeness) need to be met for this confidence interval to be valid. Is the normality condition satisfied? Explain. [2 marks]

C4: Is the representativeness condition satisfied? Could you generalize these results to other populations of lambs? Discuss. [2 marks]

C5: A previous report claimed that the average birthweight for Coopworth lambs on NZ farms is over 5.0kg. Assuming your confidence interval is valid, does it support this claim? Explain. [2 marks

After each lamb was born, its birthweight was recorded, as well as its rank (whether it was a single or twin).

The data are in the Excel file lambs.xlsx.

Use the 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 of the feeding regimes [10 marks]

A1: Use Excel to produce a table of counts for the different feeding regimes. [2 marks]

A2: Use Excel to draw an appropriate graph to display the table you created above. [2 marks]

A3: What does the graph and table tell you about the numbers of lambs from ewes in the different feeding regimes? Does it suggest that the feeding regime affects the number of lambs born to a ewe? [2 marks]

A4: Why are there not equal numbers of lambs in each feeding regime? What does this tell you about the allocation of ewes to the different feeding groups? Explain. [2 marks]

A5: Explain why the random allocation of ewes to the different feeding regimes is an important part of the experimental design. How does this random allocation affect the conclusions? [2 marks]

Part B: Exploratory analysis of birthweight [10 marks]

B1: Use Excel to draw a boxplot of birthweight for all the lambs. [2 marks]

B2: Use Excel to draw a histogram of birthweight for all the lambs. [2 marks]

B3: Use Excel to calculate the numerical summaries of birthweights of the lambs. Fill in the table with the values rounded sensibly. [2 marks]

Weight (kg)

Mean

Standard deviation

Minimum

Lower Quartile

Median

Upper Quartile

Maximum

B4: What do your plots and summary statistics tell you about birthweights of the lambs? Write one or two sentences about each of the following: centre, spread, shape and outliers. [4 marks]

Part C: Confidence interval for mean birthweight [12 marks]

C1: Calculate a 95% confidence interval for the mean birthweight of Coopworth lambs in the population. To get full marks you must show your working for the following: [4 marks]

Standard error =

Confidence interval =

Lower limit =

Upper limit =

C2: Write a sentence to interpret your confidence interval in context. [2 marks]

C3: Two conditions (normality and representativeness) need to be met for this confidence interval to be valid. Is the normality condition satisfied? Explain. [2 marks]

C4: Is the representativeness condition satisfied? Could you generalize these results to other populations of lambs? Discuss. [2 marks]

C5: A previous report claimed that the average birthweight for Coopworth lambs on NZ farms is over 5.0kg. Assuming your confidence interval is valid, does it support this claim? Explain. [2 marks

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