Dunnings PLC is a nation-wide chain of hardware stores, similar to the USA’s Home Depot.

 

Summer is firewood collecting season. Many families in rural and urban fringe areas obtain government permits to collect firewood for household use from the ground in hardwood and softwood plantation forests.

Dunnings sells a wide range of chainsaws. At the expensive end of the scale are famous brands like Stihl and Husqvarna, but there is also a market for inexpensive chainsaws. These are usually sold to people who will only need a chainsaw occasionally, perhaps once a year for a day or two to collect some firewood.

At the beginning of Summer 2021 Dunnings made a one-off purchase of a large stock of a new budget model chainsaw, the BFC9000. It sold well in the first week of its introduction.

However, over the next two weeks several of these chainsaws were returned by customers because of a serious defect. In each case the defect was a crack in the engine housing which clearly resulted from a manufacturing defect.

Dunnings management have to decide whether to recall the chainsaws that have been sold and offer repairs, replacement or refunds.

Dunnings quickly arranged for a chainsaw mechanic to examine a randomly selected sample of 60 of its inventory of thousands of the BFC9000. The mechanic reported that 9 of the chainsaws had the manufacturing defect.

Question 3a
What is the population of interest in this case?

Question 3b
Calculate a 95% confidence interval for the proportion of the entire inventory of BFC9000 chainsaws with the manufacturing defect. Show your calculations. Use the Agresti-Coull estimate of the standard error for proportions.
Question 3c
Write a short statement for decision-makers summarising your conclusions about the likely proportion of chainsaws with the defect.

Sample Solution

increasing the price of some imports of food products. If the UK leaves the EU it might be able to arrange better trade deals with the other countries, despite to some emerging economies such as China and India which are already having impact on the EU world trade graph.

Secondly, as being a member of EU for so long, UK has made lot of investments in EU and earns revenue from them. Similarly many European companies have invested in UK but due to Brexit these investments may become less charming or appealing as it will force the foreign investors to go back to EU. For example, BMW Company has already warned their workers for the potential job losses in case Brexit happens. The exchange of assets investment between UK and EU are around 89.6% but the uncertainty about Brexit has resulted into 9.9% depreciation of pound as compared to dollars. Whereas, sterling has risen by 3.6% (Oxford,2016). If only both can shake hands on some mutual successful post leaving treaties, it might then can save the investments on both sides. Another alternative solution for UK is to make a European Economic Area (EEA).

Thirdly, another issue which UK faces is the exchange of workers between EU and UK. It has generated notable stress on areas such as housing and infrastructure. Migrants who come to work from EU also contributes in the economy by filling out labour shortage gaps in areas such as nursing and teaching. So if the UK leave the EU it might lead to the immense shortage of labours as in 2016 there have been some firms who are outlining the labour shortages, especially in areas such as agriculture and construction. If UK leaves, they will gain the advantage of restricting net immigrations but on the other hand it will be difficult for UK nationals to find work abroad. According to the record, there are 2 million British nationals who are currently working in EU. Similarly according to the survey by (RICS) around 176,500 people who are working in UK from different parts of the EU will be jeopardized as well (Guardian, 2018).

Furthermore, the basic and main problem for UK is the decline of the inward investment which UK receives from the EU. Currently the value of Pound has been fallen from 10 to 15 percent showing the negative impact on the economical condition in a longer run for UK. Nevertheless, the particular problem of the decline in Pound is due to the low wage growth which has risen cost push inflation. In future if the current scenario continues it might also trigger an economic downturn for UK.

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