For the questions in the attachments below provide clear solutions with explanations in each case.

A schoolteacher is investigating the claim that class size does not affect GCSE results. His observations of nine GCSE classes are as follows: Class X1 X2 X3 X4 YI Y2 Y3 Y4 Y5 Students in class (c ) 35 32 27 21 34 30 28 24 7 Average GCSE point 5.9 4.1 2.4 1.7 6.3 5.3 3.5 2.6 1.6 score for class ( p ) Ec=238 _c' =6,884 _p=33.4 _p2 =149.62 _cp=983 (i) Determine the fitted regression line for p on c. [3] (ii) Calculate the correlation coefficient and carry out a test to establish whether or not the data agrees with the claim that class size does not affect GCSE results. [6] (iii) Following his investigation, the teacher concludes, "bigger class sizes improve GCSE results". Comment on this statement. [2] (iv) Class X5 was not included in the results above and contains 15 students. Calculate an estimate of the average GCSE point score for this individual class and specify the standard error for this estimate assuming the full normal model. [4] [Total 15]In a particular country, income tax and capital gains tax are both collected on 1 April each year in relation to gross payments made during the previous 12 months. A fixed interest bond is issued on 1 January 2003 with term of 25 years and is redeemable at 110%. The security pays a coupon of 8% per annum, payable half-yearly in arrears. An investor, who is liable to tax on income at a rate of 25% and on capital gains at a rate of 30%, bought $10,000 nominal of the stock at issue for $9,900. (i) Assuming an inflation rate of 3% per annum over the term of the bond, calculate the net real yield obtained by the investor if he holds the stock to redemption. [9] (ii) Without doing any further calculations, explain how and why your answer to (i) would alter if tax were collected on 1 June instead of 1 April each year. [2] [Total 1 1]