Essay MIS10090 – Data Analysis for Decision Makers – Data Analytics Assignment Help

Assignment Task

Question A.1
(a) For each of the following, state its level of measurement, justifying your answer in at most one sentence each:
(i) colour of a car;

(ii) dress size; 

(iii) ranking of cities as places to live;

(iv) height of a person. 

(b) Suppose that ten people rate a movie out of 5 stars, with 1 being worst and 5 being best:

2, 3, 5, 4, 5, 3, 5, 4, 1, 5

For this data set, compute the following by hand (not by spreadsheet), showing the details of your calculations:
(v) the mean;

(vi) the median; 

(vii) the mode (if any);

(viii) the range;

(ix) the variance;

(x) the standard deviation. 

From your calculations, decide whether this distribution is left-skewed, right-skewed or symmetrical. Justify your answer in at most one sentence.

(c) Give an example of a quantitative variable and another of a qualitative (categorical) variable.

Question A.2

(a) Mr Snowy’s Ice-cream van sells top-quality ice-cream, with two possible kinds of topping: chocolate or strawberry. Suppose that the probabilities that a customer orders toppings are as follows:
-Chocolate only: 0.45;
-Strawberry only: 0.1;
-Both chocolate and strawberry: 0.15.
Let C be the event that a customer orders chocolate topping and let S be the event that a customer orders strawberry topping.
(i) Are the events C and S mutually exclusive? Justify your answer in at most one sentence.

(ii) Are the events C and S independent? Justify your answer in at most one sentence.

(iii) What is the probability that a customer orders chocolate or strawberry or both?

(iv) What is the probability that a customer orders neither chocolate nor strawberry? [1 mark]

(v) Suppose that a customer orders strawberry. What is the probability that she also orders chocolate? Explain your answer in one sentence.

(d) A box contains four balls, numbered 0, 1, 2, and 3 respectively. Two balls are randomly drawn from the box without replacement. Let X be the sum of the numbers on the two balls drawn. Give the probability distribution for X in the form of a table showing each possible value for X together with the probability of X taking that value.

(e) A new test for COVID-19 has been developed. It gives either a positive or a negative result. Experiments have been carried out on the usefulness of this test, on people known to have COVID-19 and people known not to have COVID-19. The results of these experiments were:
-if the tested person has COVID-19, there is a 0.90 probability that the test will be positive;
-if the tested person does not have COVID-19, there is a 0.95 probability that the test will be negative.
Suppose that 8% of the people to be tested do in fact have COVID-19.