1. A researcher is interested to see if there is an association between year of study and the programme enrolled by students. The data collected are shown in the table below: Study Year Programme Programme Programme Programme A B C D 20 25 22 30 25 34 31 27 33 28 30 36 23 21 25 18 Use a chi-square test of independence to determine if the year of study and programme enrolled are independent at 0.05 level of significance. (23 marks) 2. The type of food favoured by deer is shown in the following table. The data were collected by an ecologist using binoculars and observation were carried out on a random sample of 300 deer. Type of food Plant composition Observed number of deer in study area feeding on this plant Sage 27% 89 Rabbit brush 35% 111 Salt brush 18% 50 Berry 11% 28 Other 9% 22 Use a 5% level of significance to test the claim that the natural distribution of plant composition fits the deer feeding pattern. (17 marks)3. A real estate manager wishes to examine the relationship between the size of a home (X: measured in square feet) and its selling price (Y). The data of 10 houses are shown in the table below: X 1400 1600 1700 1875 1100 1550 2350 2450 1425 1700 Y 245 312 279 308 199 219 405 324 319 255 (a) Calculate the least squares regression line of Y on X. (6 marks) (b) Calculate the correlation coefficient, r and coefficient of determination, (3 marks) (c) Compute the standard error of estimate S.. (2 marks) (d) Calculate the 95% confidence interval for the estimated selling price when the house size is 1250 square feet using your answer in 4(c). (6 marks) (e) Test the null hypothesis that the slope of the regression line is zero, using a 5% level of significance. (7 marks) (f) Construct the 95% confidence interval for the slope of the regression line. (6 marks)1. Distinguish between the factorial design, nested design and repeated measures design by outlining their characteristics with appropriate examples for each design. (15 marks)