STAT102 - Business Data Analysis - Facts From Figures - Statistics Assessment Answer

STAT102: Business Data Analysis Statistics Assessment Answer

Assessment Task:

Question 1 
An employee of a car salesyard is asked to choose a random sample of 50 people from a certain town and question them regarding their preference in new cars. To obtain the sample, he goes to a particular service station and questions the first 50 motorists who arrive that morning for petrol. Discuss some of the reasons why such a sample may be biased.

Question 2 
A factory makes automotive components. There are three machines (A, B and C) that make the same component. Machine A makes 40% of the components, machine B makes 35% of the components and machine C makes the other 25%. The defective rate is also known for each machine. Machine A has a defective rate of 3%, machine B has a defective rate of 2.1% and machine C has a defective rate of 1.5%. Draw a tree diagram with this information.

Question 3 
A random sample of 50 subjects were asked how many hours they had spent sleeping last week. The results showed that the times had a mean of 53 hours with a standard deviation of 10 hours. Find a 95% confidence interval for the mean time spent by all students.

Question 4
Ten eight-year-old school children were given two tests, one designed to measure IQ and the other designed to measure creativity. The test results are shown below.

Question 5
A survey was carried out in a popular supermarket at the same time over 2 periods to study price trends. The prices of 5 items were examined in the survey. Shown below are the items, their prices and the quantities used weekly by a typical household for the years 2010 and 2018.

a) Use the table above to develop unweighted aggregate price indices for 2018 using 2010 as the base year. 

b) Compute the Laspeyres price index for the year 2018 using 2010 as the base year.

c) Compute the Paasche Index number for 2018 using 2010 as the base year. 

d) What conclusions can you draw from comparing the different outcome?

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