Page 2 QUESTION ONE Every 4 months contractors are tested to see if their time in minutes to assemble a particular component have changed. The times taken to assemble the component are normally distributed. A random sample of 8 contractors was chosen and their times to assemble the component are recorded in March and in July. The data are given in the table below Contractor A March B C D E F G H 17 19 22 26 15 28 18 21 July 19 18 25 24 17 25 16 19 a. Define the terms: i. Confidence interval [2 marks] ii. Type I and Type II errors. [2 marks] b. Calculate a 95% confidence interval for the mean difference in time. [5 marks] c. Comment on the hypothesis that the two mean times for the two groups are equal. Use the 5% level of significance. [6 marks] QUESTION TWO A researcher is interested in finding out the impact of study hours on students' GPA. The following table shows the number of hours a student studies per day and the corresponding GPA of the student. Student 1 GPA Study hours 2.8 5 2 3.4 7 3 3.6 9 4 2.1 3 5 4.0 8 6 3.1 4 a. What does a scatterplot represent? [2 marks] b. Estimate a simple linear regression model and find the value of the parameters. [6 marks] c. Interpret the intercept and the slope coefficients [2 marks] d. Compute the correlation coefficient and the coefficient of determination. Interpret the coefficient of determination [5 marks]