STAT1070 Assignment 1
2017 Semester 1
Due: Electronically via Blackboard by 11:59pm, Tuesday, 11th April 2017.
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Please justify your answer to each question. This justification can involve hand calculation or providing relevant output from SPSS and/or statstar.io. If a question requires hand calculation, please show your working. If a question requires output from SPSS or statstar.io, please provide and refer to this output accordingly. Do not simply restate SPSS or statstar.io output, but provide concise interpretation of this output where appropriate, including why you used the tool you did.
Your assignment does not need a cover sheet.
You do not need to repeat the text of the question in your solution.
There is a template you can use to help structure your assignment on Blackboard.
Question 1. Types of data [6 marks]
For each of the following, give the type of data (using the types described in the section types of data in your course notes) and explain why you chose that type.
All the marks for this question are allocated to this explanation (i.e. you will receive no marks for just the correct answer without an explanation).
(a) [1 mark] pH (measure of acidity)
(b) [1 mark] A persons’ number of siblings
(c) [1 mark] The height of a tree in metres
(d) [1 mark] The time between a persons sustaining a hand-crush injury and returning to work (in weeks)
(e) [1 mark] Response to the statement Bill Shorten deserves to become Prime Minister, on the scale Strongly Disagree, Disagree, Don’t know, Agree, Strongly Agree.
(f) [1 mark] Country of Birth
Question 2. [10 marks]
Forty-four babies – a new record – were born in one 24-hour period at the Mater Mothers’ Hospital in Brisbane, Queensland, Australia, on December 18, 1997. For each of the 44 babies, The Sunday Mail recorded the time of birth, the sex of the child, and the birth weight in grams. These data are available in the file baby-boom.sav
The variables in the file are
sex Sex of the child (1 = girl, 2 = boy)
weight Birth weight in grams
minutes Number of minutes after midnight of each birth
(a) (i) [3 marks] Using appropriate graphs and descriptive (also known as summary) statistics, describe the distribution of minutes.
(ii) [3 marks] Using appropriate graphs and descriptive (also known as summary) statistics, describe the distribution of weight.
(b) [2 marks] Describe the relationship (if any) between sex and weight. Construct a graph (using software) in support of your answer. If you conclude there is no relationship, you must describe the features of the data that indicate this.
(c) [2 marks] Describe the relationship (if any) between minutes and weight. Construct a graph (using software) in support of your answer. If you conclude there is no relationship, you must describe the features of the data that indicate this.tat70
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Question 3. [14 marks]
Consider a screening test for a disease.
The sensitivity of the test is 80%.
The specificity of the test is 95%.
The disease is present in 0.1% of the population.
Use the following events for a patient receiving the screening test;
D they have the disease
DC they do not have the disease
P their test gives a positive result
PC their test gives a negative result
(a) [3 marks] Write the three statements given in the introduction of the question as probability or conditional probability statements (whichever is appropriate), using the events above.
(b) [2 marks] What is the probability a patient has the disease and their test gives a positive result? Show working.
(c) [3 marks] What is the probability a patient does not have the disease and their test gives a positive result? Show working.
(d) [2 marks] What is the probability that a patient receives a positive result? Show working.
(e) [2 marks] If a patient receives a positive result, what is the probability that they have the disease? Show working.
(f) [2 marks] What does this suggest about the screening test?
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Question 4. [10 marks]
Agricultural scientists are working on developing an improved variety of Roma tomatoes. Market research has indicated that customers are likely to bypass Romas that weigh less than 70 grams. The current variety produces fruit that average 74.0 grams with a standard deviation of 3.3 grams.
(a) [2 marks] Assuming that the normal distribution is a reasonable model for the weights of these tomatoes, what proportion of Roma tomatoes are currently undersize (less than 70g)?
(b) [3 marks] The aim of the current research is to reduce the proportion of undersized tomatoes to no more than 4%. One way of reducing this proportion is to raise the average size of the fruit. If the standard deviation remains the same, what must the target mean be to achieve the 4% goal?
(c) [3 marks] Another way of reducing the proportion of undersized tomatoes is to reduce the standard deviation. If the average size of the fruit remains 74.0 grams, what must the target standard deviation be to achieve the 4% goal?
(d) [2 marks] Assuming that the goal of 4% undersized tomatoes is reached, what is the probability of getting no more than 1 undersized tomato in a randomly selected sample of 20 tomatoes?
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