STAT 170 Assignment 01

A market research company conducted a survey of 200 households in a large city. The aim was to investigate the viability of setting up a new DVD rental service. Use the information below, which describes some of the variables recorded in this study to answer Questions 1 and 2.

Variable                               Description

ID                                  ID number for household

PreSchoolers                   Pre-school children in household:

                                                             0 = No,  1 = Yes

Children                                      Number of children aged under 18 years living in household

Adults                                         Number of adults aged 18 years or older living in household                 

Income                           Combined annual income of household

PayTV                            Pay TV provider:

                                                 1 = do not subscribe to Pay TV, 2 = BOXTEL,

                                                 3 = Catch TV, 4 = T-Fox, 5 = other provider

Rental:                           Likelihood of household renting DVDs from a DVD rental service in a typical week:

                                                 1 = extremely likely, 2 = very likely,

                                                 3 = moderately likely, 4 = slightly likely,    

                                                 5 = not at all likely

NumDVDs:                                  Number of DVDs typically rented from a DVD rental service in a week.

Question 1 (8 marks)

a.  If possible, list one variable from those described above which is:

a.  Describe an appropriate target population for this survey.

a.  Do you think the sample would have been randomly selected from this target population?  Explain your answer.

a.    Write down the name of an appropriate graph to use to investigate:

                     i.        the relation between the combined annual income of household members and the likelihood of the household renting DVDs from a DVD rental service in a typical week (Income and Rental).

                     i.        the relation between whether there are any pre-school children in the household and the likelihood of the household renting DVDs from a DVD rental service in a typical week (PreSchoolers and Rental). 

                     i.        the combined annual income of household members and the number of DVDs typically rented from a DVD rental service in a week. (Income and NumDVDs). 

Question 2 (4 marks)

The following table summarises the responses to the survey questions regarding whether the household has any pre-school children and the likelihood of the household renting DVDs in a typical week.

Tabulated Statistics: PreSchoolers, Rental

Rows: PreSchoolers   Columns: Rental

     ExtremelyLikely  VeryLikely  ModLikely  SlightlyLikely  NotLikely     All

No                25          20         24              23         38     130

Yes               23          14         15              10          8      70

All               48          34         39              33         46     200

a.  What proportion of households are extremely likely to rent DVDs from a DVD rental service in a typical week?

a.  What proportion of households with pre-school children are extremely likely to rent DVDs from a DVD rental service in a typical week?

Question 3 (12 marks)

The Nordic Ecolabel is the official Ecolabel of the Nordic countries and was established in 1989 by the Nordic Council of Ministers. The Nordic Ecolabel evaluates a product's impact on the environment throughout the whole life cycle. The label guarantees among other things that climate requirements are taken into account, and that CO2 emissions (and other harmful gasses) are limited. The "Swan" symbol, as it is known in Nordic countries, is available for a large number of product groups. Companies can obtain the right to use the Nordic Ecolabel on their
product via a licensing process. Environmental criteria, performance criteria and quality and regulatory criteria must be satisfied. 

A Nordic Ecolabelled bakery is a bakery that has been awarded a Nordic Ecolabel licence subject to strict requirements that cover the entire business. Criteria are set on ingredients, energy use, packaging, transport, cleaning chemicals, the working environment and waste management. A Nordic Ecolabelled bakery must ensure that the manufacturing of the bread has a low environmental impact from a life cycle perspective. This applies to the baking as well as the supplier chain. One of the requirements is that the total energy use in the bakery’s production process should not exceed 1.50 kilowatts per hour per kg. Another is that at least 95% of the palm oil used in the bakery must be certified according to a standard that includes balancing financial, ecological and social interests and this standard must promote and contribute towards sustainable forestry agriculture.

A study of Bread Basket Bakeries, a chain of Nordic bakeries, found that the average amount of energy used in their bakeries follows a normal distribution with a mean of 2 kilowatts per hour per kg and a standard deviation of 0.75 kilowatts per hour per kg.  Show your working, including appropriate diagrams, to answer the questions on the following page.

Question 3 continued

a.    Find the probability that a randomly selected Bread Basket Bakery would be eligible to carry the Nordic Ecolabel.

a.    Find the probability that a randomly selected Bread Basket Bakery uses between 1.25 and 1.75 kilowatts of energy per hour per kg

a.    Managers of Bread Basket Bakeries with energy consumption higher than the 85^th percentile of the company’s energy consumption distribution must attend a workshop aimed to reduce energy use. Find the amount of energy used beyond which managers are expected to attend this workshop.

a.    Find the probability that a random sample of 10 Bread Basket Bakeries will have an average energy consumption that would be acceptable for Nordic Ecolabelling.