Question

Question 2 (a)() All of the employees of a company have been given training on a new regulatory regime. Twenty employees selected at random are tested on their knowledge of this topic. The sample average score for these twenty employees is 36.6 and the sample standard deviation is 24.9 All of the employees will be given a similar test. Assuming that the scores are normally distributed, find a 95% confidence interval for the average score of all the company's employees (5 marks) (ii) Explain why you use a t-statistic in your calculations in (a) (i) above (3 marks) (b) An IT service company is investigating the awareness among training companies of a training support package that it markets. It has found the percentages of large, medium-sized and small training companies that have heard about the package from different sources. These are Source Advertising Word of mouth Other Large Medium Small 85 41 80 Using an additive model, calculate the percentage of all small companies that have heard about the package through advertising (5 marks) (c) An opinion polling company is investigating the approval rating of a political leader. It wishes to estimate the proportion of all voters who approve of his performance, and wants to find a 95% confidence interval for this proportion (which is believed to be about 40%). Calculate the size of the sample needed to give a 95% confidence interval with a width of 4 percentage points. As an example, if 40% of all voters approved of his performance then the 95% confidence interval would be (38%, 42%) (6 marks) (d) You are given the following incomplete ANOVA table ANOVA Source Treatment A Treatment B Interaction Error Total df MS 0.86976 1.71731 1.79086 1775.9 10970.0 66421.74 3 510.46 Do calculations to find how many observations this ANOVA table is based on. (6 marks) (Total 25 marks)

Answer 1

all gcosme =36.6 S 24.q 2.013 as An 36-6 土2.043 x24.9 2-o (24-45, 48.25 Scanner