Kindly assist me to answer the following questions. Thank you

[15] Eight pairs of slow learners with similar reading capabilities are identified in a third grade class. One member of each pair is randomly assigned to the standard teaching method, while the other is assigned to a new teaching method. The scores are as given below. Pair 2 3 4 5 6 7 New Method 77 74 82 73 87 66 80 Old Method 72 68 76 84 68 64 76 Test for the difference between mean scores for the two methods (6) Test for the cquality of variances for these two methods (4) Obtain the 95% of confidence interval for the difference in means. (2) [12] A survey was conducted to investigate whether people tend to marry partners of about the same age. This question was addressed to 12 married couples and their ages were given in the following table. Couple No. 5 6 11 12 Husband's are ix) 37 36 51 36 Wife's age (y) 35 37 50 46 36 42 46 35 Draw the scatter plot and comment on it (1) Find the correlation coefficient and interpret it (4) If p represents the population correlation coefficient between the ages of partners, test (3) the significance of p at 5% level [8] A study was made on the effect of temperature on the yield of a chemical process. The following data (in coded form) were collected X: -5 -4 -3 - 1 0 4 y : 5 4 10 13 14 13 Linear regression model y = Bo + 1 x te is fitted for the above data. Describe the parameters and variables in the model (1) Obtain the least squares estimates of By and , and hence the prediction equation. (3) Construct ANOVA table and test Hy : B, - 0 at 5% level of significance (3) What are 95% confidence limits for ? (2) What are the confidence limits for the true mean value of y when x = 3 at 95% (2) confidence level? Are there any indications that a better model can be tried? (2) [13]