Question

Question Four Total 25 Marks 4 marks (i) Distinguish between Type I and Type Il errors in hypothesis testing (i) Nineteen employees working in the call centre of a bank were chosen at random from the workforce and agreed to assist in the assessment of two different training programmes (A and B).Each employee was then given a performance score (measuring a range of aspects of their work) expressed as a mark out of a possible maximum of 100. The results were as follows: Training programme A Training programme B Performance scores 64 55 57 73 51 60 62 78 68 63 79 60 75 89 58 75 72 84 69 724 Totals 568 Conduct a test at the 5% to investigate whether differences exist between the two training programmes and comment briefly on your findings. 17 marks (ii) At the end of the skiing season the tourist board in a mountain region examines the records of ten ski resorts. For each one it obtains the total number (v, thousands) of visitor-days during the season as a measure of the resort's popularity, and the ski-lift capacity (x, thousands), being the maximum number of skiers that can be transported per hour. The resulting data are given in the following table: Resort: Lift capacity x Visitor-days y: 1.9 3.3 1.2 4. 1.5 2.2 1.0 5.6 1.9 3.8 15.1 22.6 9.2 37.5 8.9 21.1 5.8 410 9.2 32.4 2x 26.6, x 91.08, y 202.8, y 5603.12, Exy NB: you are NOT asked to verify these results 707.58 (a) Draw a scatterplot of y against x and comment briefly on any relationship between a resort's popularity and its ski-lift capacity [4 marksl (5 marks) 2 marks] (b) Calculate the correlation coefficient and the coefficient of determination between x and y and comment briefly in the light of your comment in part (). (c) Calculate the fitted linear regression equation of y on x

Answer 1