Business Statistics Assignment
Question 1 -
An automobile association is interested in the opinions of its members about the introduction of a new type of roadside assistance package which gives the members, for an extra annual fee, additional services to those currently provided. Specifically, the association wants to know what proportion of members plan to buy the new package. The association took a random sample of 15,000 members from its database and sent them an e-mail with a request to fill out a survey, in exchange for a 10% discount voucher to use at the association's shop. Of the members that were sent the e-mail, 7,330 replied of which 2,932 indicated that they would purchase the new package.
a) What is the population of interest?
b) What is the parameter of interest?
c) What is the sampling method used?
d) What is the sample?
e) What is the statistic and its value?
f) The association has now decided that different levels of membership may have different opinions. Of their members 50% are bronze-level, 25% are silver-level, 15% are gold-level and 10% are platinum-level. How might the association choose a suitable sample?
Question 2
In recent times inner city living has become more popular in Australian cities as people want to live closer to their work and the additional facilities that a city has to offer. This trend has led to an explosion in apartment developments to such an extent that there is now an oversupply of apartments in some cities. A comparison of two-bedroom apartment prices in some of the cities may give potential buyers an idea of how the cost of living in the CBD in these cities can be compared.
The file 'Apartment.xlsx' (under Assessment folder on Moodle site) contains the prices ($000s) for a sample of 203 two bedroom apartments listed for open inspection on a real estate website on Saturday 16th July 2016; 20 in the Adelaide CBD , 56 in the Brisbane CBD, 74 in the Melbourne CBD, and 53 in the Perth CBD.
a) Use Excel to obtain the Descriptive Statistics for the variable Price for "all cities apartment prices" and for each city's apartment prices. Record the values in Table 1 below (Values must be reported to 2 decimal places).
b) Use Excel to produce a histogram for "all cities apartment prices" and for each city's apartment prices (Use class widths of $50,000).
c) Examine the histograms and record the results for 'all cities' and for each of the cities Adelaide, Brisbane, Melbourne, and Perth in Table 1 below.
d) Which measure of centre do you think is the most appropriate to use to compare the two- bedroom apartment prices? Why?
e) Which city has the highest prices? Why? Write down this value and interpret it.
f) Which measure of spread do you think is the most appropriate to use to compare the apartment prices? Why?
g) Which city has the most variability in prices? Why? Write down this value and interpret it.
h) Use the appropriate values in Table 1 below and the ABS_2007_Box_Plot_Tool Excel file (under Supplementary Material folder on Moodle site) to construct side-by-side boxplots for "all city apartment prices" and for each city's apartment prices.
i) How many outliers can be identified in the side-by-side boxplots? (Hint: You are required to calculate the lower and upper fence for each boxplot in the side-by-side boxplots)
Table 1: Comparison of two bedroom apartment prices by city
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Shape
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Centre
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Spread
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City
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Describe the shape of the data
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Mean
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Median
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Standard Deviation
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Q1
&
Q3
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IQR
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Min
&
Max
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Range
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All cities
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Adelaide
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Brisbane
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Melbourne
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Perth
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Question 3 -
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
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Number of Vehicles Involved
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Did alcohol play a role?
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1
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2
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3
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Totals
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Yes
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50
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100
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20
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170
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No
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25
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175
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30
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230
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Totals
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75
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275
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50
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400
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All answers must be reported to 4 decimal places.
a) Given a randomly chosen accident,
1) What is the probability that the accident didn't involve alcohol?
2) What is the probability that the accident involved more than one vehicle?
3) What is the probability that the accident involved alcohol and a single vehicle?
4) What is the probability that the accident involved alcohol or two vehicles?
5) If alcohol was involved, what is the probability that the accidents involved a single vehicle?
6) If 3 vehicles were involved, what is the probability that the accidents didn't involve alcohol?
b) Are the events "alcohol involved in an accident" and "single vehicle involved in an accident" mutually exclusive?
c) Are the events alcohol involved in an accident" and "single vehicle involved in an accident" independent?
Question 4 -
Olivia's restaurants serve a lot of pasta. They have found that the daily demand for pasta for each restaurant follows a Normal distribution with a mean of 8.5kg and a standard deviation of 0.94kg.
Let X represent the daily demand for pasta for each restaurant (kg)
Then X ∼ N(8.5, 0.94)
What is the probability that a restaurant uses
1) less than 8kg?
2) more than 9.3kg?
3) less than 9.1kg?
4) more than 8.2kg?
5) between 8.1kg and 9.5kg?
6) between 8.5kg and 10kg?
Attachment:- Excel.rar