Question 1

Companies which adopt a green policy contribute to our environment and enhance our well-being. However, many times, production costs of green companies are higher than those which are not. That may affect product prices. The additional production cost can, sometimes, be compensated by customers’ preferences for products which are labelled as environment friendly.

Assume that you are a manager of a paper company. You consider adopting a green policy. The environment-friendly  changes  in  the  paper  production  process  are  expected  to  increase  the production costs, which would result in an increase in the price from £5 for a pack of a4 sheets to £7. Before making any changes, your company ran a survey. 110 participants were asked whether

i.       They consider environmental issues important

ii.       They would buy an A4 paper pack for £7 instead of £5, if the £7 pack had an ‘environment

friendly’ label stamp on it and the £5 pack did not.

The results of the survey are given in the following table.

a. Is people’s intention to buy paper with a green label for £7 instead of paper without a green label for £5 independent from their views about the importance of environmental issues?

To gain a better understanding of the relation between customer’s views and their intention to buy green labelled paper for a higher price, another survey was performed. This time, participants were asked to rate the likelihood (as a percentage) that they would buy paper given different prices. For each of 4 different prices, the mean purchase likelihood was calculated. The mean of purchase likelihood and prices are given in the following table.

Calculating the regression coefficients in Excel, the following output was obtained.

b. Write down a linear regression model for the relationship between purchase likelihood rating and price.

c. What percentage of the variance in the mean purchase likelihood ratings can be explained by the price?

d. Is there a significant relationship? Use α=0.05, and specify your hypotheses.

Question 2

Imagine that you are the manager of a DIY furniture store. Each high quality table of a certain model is made of wood of two types: wood type A is used to make the top of the table, and wood type B is used to make the four legs of the table. The price of the amount of wood A required for the top is normally distributed with mean £100 and std £15. The price of the amount of wood B

required for each of the legs is normally distributed with mean £12 and std £2. Assume that the prices of the two types of wood are independent.

a. Calculate the mean and standard deviation of the price of the wood required for a table.

b. What is the probability that the price of the wood required for the production of a whole table is larger than £182?

c. It is essential that the number of screws and bolts in each pack is the number required for the assembly of the table or larger than it. The probability that the number of screws and bolts in the pack is correct (or larger than the number required) is 0.99.

Assume that the number of bolts and screws in each pack is independent or the number of bolts and screws in different packs.

If an office orders 10 tables, what is the probability that in one of the packs, at least one screw or bolt is missing?

d. The number of chairs of a specific model sold per day was sampled on 25 randomly chosen days during the last year. The standard deviation obtained in the sample was 11, and the mean was 45. Assume that the number of chairs sold per day follows a normal distribution. Construct an 80% confidence interval for the mean number of chairs sold per day.

e. The number of chairs of the same model sold per day had been sampled on 25 randomly chosen days during the previous year. Back then, the mean was 47. Did the number of chairs sold per day decrease?