SCI1020 – Introduction to Statistical Reasoning ASSIGNMENT 2 – Semester 1, 2018  This assignment counts 5% towards the assessment in this unit.  It contains material from Chs 9, 15, 16-22 of the...

SCI1020 – Introduction to Statistical Reasoning ASSIGNMENT 2 – Semester 1, 2018

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   This assignment counts 5% towards the assessment in this unit.
  

  
  


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   It contains material from Chs 9, 15, 16-22 of the Moore text 7th ed. (Chs 9, 11, 14-20 of 6th ed.)
  

  
  


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   Statistical tables may be needed. These are available in the Moore text. Your work should be
  

  
  

  presented in a neat and readable fashion.
  

  
  


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   It is meant to be individual work and MUST be accompanied by a signed assessment
  

  
  

  coversheet. A copy of this assignment is on the SCI1020 Moodle page in the block
  

  
  

  “Assignments”.
  

  
  


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   The completed assignment should be placed in your Tutors’ submission box on the ground
  

  
  

DUE DATE: NOON on MONDAY, 21 May 2018 (Wk 12).

floor of 9 Rnf Walk.

Question 1 (10 Marks)

TOTAL MARKS = 75

Fractures of the spine are common and serious among women with advanced osteoporosis (low mineral density in the bones). Researchers wanted to know if taking a strontium ionic compound would help prevent this.

A large medical trial was undertaken at 2 medical clinics in two different countries. A total of 1700 women, 900 Australians and 800 Malaysians with this condition were randomly assigned to take either a strontium compound or a placebo each day. All the subjects had osteoporosis and had suffered at least one fracture. All were taking calcium supplements and were receiving standard medical care. The measurements done were initial bone density and bone density after three years on the treatments. The number of new fractures in that time was also counted.

The normal diets in the two countries may be different and so may influence these variables.

1. 
   

   a) Name the explanatory and response variables in this study.
   

   
   


2. 
   

   b) What is the population of interest in this study?
   

   
   


3. 
   

   c) Identify a confounding variable.
   

   
   


4. 
   

   d) Outline a blocked randomized design for this experiment, clearly describing all the important features needed in any well-designed experiment.
   

   
   

Question 2 (12 marks)

According to internal testing done by the Get-A-Grip tyre company over many years, the mean lifetime of tyres sold on new cars is normally distributed with a mean of 37,000 kilometres and a standard deviation of 4,000 kilometres.

a) What is the probability of a random new car with these tyres lasting for 40,000 km or more?

If this is true, then we would like to know what mean kilometres of tyre-lifetimes are likely to occur for the university’s fleet of 100 such cars (a random sample of the new cars involved).

b) If the claim by Get-A-Grip is true, what is the mean of the sampling distribution of x for samples of size n = 100?

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c) If the claim by Get-A-Grip is true, what is the standard deviation of the sampling distribution of x for samples of size n = 100?

4. 
   

   d) Sketch this sampling distribution.
   

   
   


5. 
   

   e) What is the probability that such a sample of 100 cars would have an average kilometres of tyre-lifetimes greater than 40,000km?
   

   
   


6. 
   

   f) If the population distribution was really skewed and not Normal, EXPLAIN whether or not these probability calculations on the sample of 100 cars still validly be done. State the concept or theory that is involved in this situation.
   

   
   


7. 
   

   g) On the same sketch in part d) above sketch the distribution that would result for the same population if the sample size was n = 400.
   

   
   

Question 3 (18 marks)

Many people have high anxiety about visiting the dentist. Researchers want to know if this affects blood pressure in such a way that the mean blood pressure while waiting to see the dentist is higher than it is an hour after the visit. Ten individuals have their systolic blood pressures measured while they are in the dentist’s waiting room and again an hour after the conclusion of the visit to the dentist. The data are as follows:

1. 
   

   a) Are these data paired or unpaired? What type of study design was this?
   

   
   


2. 
   

   b) What conditions are needed to proceed with inference using this data? What type of plot would be necessary as a check? Perform a basic, quick check to show that the conditions are valid.
   

   
   


3. 
   

   c) Calculate the relevant summary statistics from the data? (calculator may be needed)
   

   
   


4. 
   

   d) Calculate a 95% confidence interval for the mean change in systolic blood pressure on visiting the dentist. Show all your working.
   

   
   


5. 
   

   e) Based on that confidence interval, is there sufficient evidence to conclude that systolic blood pressure has fallen an hour after the visit?
   

   
   


6. 
   

   f) Conduct a test of significance (at a significance level of 5%) to determine if there is an increase in blood pressure before visiting the dentist compared to after. Follow all steps clearly and write a clear conclusion.
   

   
   

Question 4 (18 marks)

The amino acid lysine has important nutritional value in food for animals. Ordinary corn does not have much lysine in it. Researchers developed a new variety of corn which did have higher lysine content. They wished to test whether the new “high-lysine” corn was a better feed for animals such as chickens.

An experimental group of a 20 randomly chosen one-day old chickens was fed the “high- lysine” corn. A separate control group of another 20 randomly selected one-day old chickens was fed the “ordinary” corn. All other features such as amount of feed, time and frequency of feeding and environment were identical between the two groups.

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The weight gained (in grams) by the chickens after 21 days on these diets was measured. The data (below) is also in an Excel file, “Lysine in corn” (available in Moodle in the “Assignments and project” block).

Control group Experimental Group

1. 
   

   a) Does this design use paired data or independent samples? Explain.
   

   
   


2. 
   

   b) Compute a 90% confidence interval for the mean weight gain in ONLY the “high- lysine” corn-feed chickens. Show all your working.
   

   
   


3. 
   

   c) The researchers were striving (unofficially) to achieve a mean weight gain of 410g by using the high-lysine corn. Based on this confidence interval, explain if they have achieved this?
   

   
   


4. 
   

   d) Conduct a test of significance (at a significance level of 5%) on the difference between the two corn types to decide whether there is a greater mean weight gain by “high-lysine” corn-feed chickens compared to the ordinary corn-feed. Follow all steps clearly and write a clear conclusion.
   

   
   

Question 5 (17 marks)

Wild fruit flies have red eyes. A recessive mutation produces white-eyed individuals. A researcher wants to assess the proportion of heterozygous individuals. A heterozygous red-eyed fly can be identified through its off-spring. When crossed with a white-eyed fly it will have a mixed progeny.

A random sample of 100 red-eyed fruit flies was taken. Each was crossed with a white- eyed fly. Of the sample flies, 11 were shown to be heterozygous because they produced mixed progeny.

1. 
   

   a) Check this data for the conditions necessary for the calculation of a large-sample confidence interval. Does it comply OR should you use the plus-four interval only?
   

   
   


2. 
   

   b) Determine a 95% confidence interval for the proportion
   

   
   


3. 
   

   c) Also use a test of significance at 5% to test the hypothesis that the proportion of heterozygous red-eyed flies is different from 10 %?
   

   
   


4. 
   

   d) Compare the answer from this test at 5% in c) to that from the 95% confidence interval in b). Would you necessarily expect the same answer?
   

   
   

   ------------------------ (end of assignment questions) ----------------------
   

   
   

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