QUESTION one [so MARKS) 1.1.A supplier of a household disinfectant liquid launched a promotional campaign to increase sales of its 500 ml bottles. Before the campaign, the average weekly sales (in cases sold) were recorded at 12 randomly chosen retail outlets throughout KwaZulu-Natal. Three weeks after the campaign, average weekly sales were again recorded at the same 12 outlets. The average weekly sales (in cases sold) are shown for each of the 12 retai outlets as follows: Sales in cases per outlet before and after the promotional campaign. OUTLET A B C D E F G H | J K L SALES (before) 12 8 14 9 13 15 10 12 10 13 12 10 SALES (after) 12 11 14 9 11 16 11 13 11 13 14 11 Can the suppliers of the household disinfectant conclude that the promotional campaign has been a success? Test this management question statistically. Formulate the nu | and alternative hypotheses to answer this management question. Conduct a matched-pairs t-test at the 5% significance level. What is your conclusion? (15] 1.2. Chester Butchery supplies Vienna sausages in the entire of KZN province. A meat packer is investigating the marked mass shown on Vienna sausages. A pilot study showed a mean of 11.8kg per pack and a variance of 0.49kg. How many packs should be sampled in order to be 92% confident that the sample mean will differ by at most n.2kg? (15) QUESTION TWO [30 MARKS) 2.1. On average, a 60 minutes radio show has 45 minutes of actual programme. Let's assume that the probability distribution of the number of minutes of actual radio programme is uniformly distributed with a range of 40 minutes to 50 minutes. i. Compute the probability that the show will have at least 48 min of actual programming time (3) ii. Compute the standard deviation. (3) iii. Drawthe graph offix) clearly labelling the axes (4) 2.2. A major metropolitan newspaper selected a simple random sample of 2000 readers from their list of 20000 subscribers. They asked whether the paper should increase its coverage of local news. Seventy percent ofthe sample did not support the idea of more local news coverage. What is the 94% confidence interval for the proportion of readers who would like more coverage of local news? (10) 2.3. The operations manager ofa computer accessories firm with branches in Cape Town and Durban wants to establish whether their Cape Town branch is performing better than their Durban branch in terms of the average Size oforders received, Both branches have been operating for only one year. A random sample of 17 orders from the Cape Town branch had an average value of RBBSJO With a standard deviation equal to R121,50. Orders received by the Durban branch of the firm were also randomly sampled. The average of the 15 orders sampled was R265,60 with a sample standard deviation oleSZlD. Can the operations manager conclude, atthe 5% significance level, that the Cape Town branch is performing better than the Durban branch? Show the null and alternative hypothv" for the test and draw the appropriate conclusion. 4/4 QUESTION Tints: (30 mass: 3.1.Milk cartons are advertised to contain one litre of milk, From a randomly sample of 18 one-litre cartons whose contents were accurately measured by the South African Bureau of Standards (SABS), it was found that the average fill was 098 litres with a sample standard deviation of 0,052 litres. Assume that the fill of onevlitre milk cartons is normally distributed. i. Using a 99% confidence level, estimate theactual mean fill of all one-litre milk cartons. Interpret your findings and comment on the question. (4) li. Repeat the exercise in Ii} above, but use 90% confidence level. (4) iii. Explain any differences in the findings computed above, [2) 3.2,A random sample of 300 Status cheque accounts at Capital Bank showed that 48 were overdrawn. When 250 Elite cheque accounts at the same bank were randomly checked, it was found that 55 were overdrawn, Can the bank manager conclude that more Elite cheque account clients, proportionately. are likely to be overdrawn than Status cheque account clients? Test this hypothesis at the 4% level of significance. What conclusion can be drawn? 10}