Statistics

Statistics
Q1. [9 Marks]

The file “SALES” contains weekly sales figures for 2012 for a newly introduced 1 litre carton of orange juice at a large suburban supermarket in Perth.

a) Use Excel to construct a histogram of the data.

b) Comment on the weekly sales figures for this newly introduced orange juice, using the information from (a).

Q2. [9 Marks]

The following table contains data for the number of withdrawals from a bank in an industrial area.

Year Withdrawals ($ ten thousands)
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009 23.6
18.3
26.0
24.9
28.1
25.3
29.1
24.7
30.1
27.8
a) Provide a graphical display of the data that will be suitable for examining the trend in the number of withdrawals over the given time period.
b) From your graph, describe any trends you observe.

 
Q3. [12 Marks]

The manufacturer of Boston and Vermont asphalt shingles provides its customers with a 20-year warranty on most of its products. To determine whether a shingle will last as long as the warranty period, accelerated-life testing is conducted at the manufacturing plant. Accelerated-life testing exposes a shingle to the stresses it would be subject to in a lifetime of normal use via an experiment in a laboratory setting that takes only a few minutes to conduct. In this test, a shingle is repeatedly scraped with a brush for a short period of time, and the shingle granules removed by the brushing are weighed (in grams). Shingles that experience low amounts of granule loss are expected to last longer in normal use than shingles that experience high amounts of granule loss. In this situation, a shingle should experience no more than 0.8 gram of granule loss if it is expected to last the length of the warranty period. The file “GRANULE” contains a sample of 170 measurements made on the company’s Boston shingles and 140 measurements made on Vermont shingles.

(a) List the five-number summaries for the Boston shingles and for the Vermont shingles.
(b) Construct Boxplots for the two brands of shingles and describe the shapes of the distributions.
(c) Comment on the ability of each type of shingle to achieve a granule loss of 0.8 gram or less.
Q4. [12 Marks]

A tyre manufacturer believes that the tread-life of its snow tyres can be described by a Normal Model with a mean of 32,000 miles and standard deviation of 2500 miles.

a) If a person buys a set of these tyres, would it be reasonable for him to expect they’ll last 40,000 miles?
b) Approximately what fraction of these tyres can be expected to last less than 30,000 miles?
c) Approximately what fraction of these tyres can be expected to last between 30,000 and 35,000 miles?
d) Estimate the inter quartile range (IQR) of the tread-lives.
e) In planning a marketing strategy, a local tyre dealer wants to offer a refund to any customer whose tyres fail to last a certain number of miles. However, the dealer does not want to take too big a risk. If the dealer is willing to give refunds to no more than 1 of every 25 customers, for what mileage can he guarantee these tyres to last?
Q5. [8 Marks]

Each year, ratings are complied concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether a car needs warranty-related repair(Yes, No) and the country in which the company manufacturing a car is (United States or Not United States).

Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that the car was manufactured by a US –based company is 0.60 and the probability that the new car needs a warranty repair and was manufactured by a US –based company is 0.025.

(a) Construct a contingency table to evaluate the probabilities of warranty-related repair.

A new car (within 90 days of sale) is chosen at random. Use your contingency table to answer the following questions:

(b) Needs a warranty repair?
(c) Needs a warranty repair and was manufactured by a US –based company?
(d) Needs a warranty repair or was manufactured by a US –based company?
(e) Needs a warranty repair or was not manufactured by a US –based company?

 

 

 

 

 

 

 

 

 

Q6. [10 marks]
The Australian quarterly total sales of wine (in millions of litres) and a quarterly Wine Price Index(WPI) are listed here for the 10 quarters from December 2002 to March 2005.

Wine Sales WPI
97.6
71.4
86.7
92.0
99.2
76.2
87.7
95.3
103.7
76.4 156.0
153.7
155.6
157.0
158.3
156.4
159.1
161.0
162.6
159.5

a) Using Excel, produce a scatterplot of this data, including least-squares line, and full regression statistics.
b) Estimate the quarterly total sales of wine when the WPI is 155.0.
c) If an economist predicts that quarterly total wine sales should reach 105 million litres for a WPI of 165.0, comment on whether the prediction would be a valid use of this analysis.
d) There are some assumptions involved in using a linear regression model. Do you think they are reasonable for this case? Why?
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