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 KwaZuluNatal. 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 ofthe 12 retail 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 S 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 null and alternative hypotheses to answer this management question. Conduct a matched-pairs t- test at the 5% signicance 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% condent that the sample mean will differ by at most 0.2kg? (15) 2.1.IOn 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 least48 min ofactual programming time (3) ii. Compute the standard deviation. (3) iii. Draw the graph off(x) 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 of the sample did not support the idea of more local news coverage. What is the 94% condence interval for the proportion of readers who would like more coverage oflocal news? (10) 23. The operations manager of a computer accessories rm with branches in Cape Town and Durban wants to establish whether their Cape Town branch is performing better than their Durban branch in terms ofthe average size of orders 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 R335.20 with a standard deviation equal to R121.50. Orders received by the Durban branch of the rm were also randomly sampled. The average of the 15 orders sampled was R265.60 with a sample standard deviation of R152.20. Can the operations manager conclude, at the 5% signicance level, that the Cape Town branch is performing better than the Durban branch? Show the null and alternative hypotheses for the test and draw the appropriate conclusion