# Quantitative Skills for Business – Statistics Assignment

Interna Code – MAS1613

## Statistics Assignment

Question 1 :

A manufacturer of DVD players purchases a particular microchip, called the DV-6, from three suppliers; Perth Electronics, Sound Sales and Critical Components. Thirty percent of the DV-6 chips are purchased from Perth Electronics, 20 percent from Sound Sales and the remaining 50 percent from Critical Components. The manufacturer has extensive histories on the three suppliers and knows that 3 percent of the DV-6 chips from Perth Electronics are defective, 5 percent of chips from Sound Sales are defective and 4 percent of the chips purchased from Critical Components are defective.
When the DV-6 chips arrive at the manufacturer, they are placed directly in a bin and not inspected or otherwise identified by the supplier.

a) Summarise the above information in event notation from the three suppliers A1, A2, A3.

b) List the three prior probabilities of these events.

c) List the additional information concerning the DV-6 chip (ie: event B1). List the conditional probabilities.

d) When the DV-6 chips arrive at the manufacturer, they are placed directly in a bin a not inspected or otherwise identified by the supplier. A worker selects a chip for installation in a DVD player and finds it defective. What is the probability that it was manufactured by Sound Sales?

Question 2 :

The variables are defined as:

Data Set 1 – Real Estate
X1 = Selling price in \$000
X2= Number of bedrooms
X3= Size of the home in square feet
X4= Pool (1=yes, 0=no)
X5= Distance from the centre of the city
X6= Township
X7= Garage attached (1=yes, 0=no)
X8= Number of bathrooms

1. Develop a 95 percent confidence interval for the mean selling price of the homes.

2. A recent article in the Stirling Times reported that the mean size of the homes was more than 2,100 square feet. Can we conclude that the mean size of the homes sold in the Eastern suburbs area is more than 2,100 square feet? Use the .01 significance level. What is the p-value?

3. Determine the proportion of homes that have an attached garage. At the .05 significance level, can we conclude that more than 60 percent of the homes have an attached garage?What is the p-value?