The following data gives the total December snow cover (in million km2 ) in a particular country for last fifteen years. Assume that the population follows a normal distribution N(,2). (a) Find unbiased estimates for and 2. (4 marks) (b) Test if we should accept >9 under 5% significance level. You need to state the null and alternative hypotheses; report p-value and make a conclusion on it. (10 marks) (c) Find a two-sided 95% confidence interval for . (4 marks) (d) Find a lower 95\% confidence interval for 2. (4 marks) (e) Under 5% significance level, test whether =3. You need to state the null and alternative hypotheses and make a conclusion on it. (10 marks) (32 marks) The following data gives the total December snow cover (in million km2 ) in a particular country for last fifteen years. Assume that the population follows a normal distribution N(,2). (a) Find unbiased estimates for and 2. (4 marks) (b) Test if we should accept >9 under 5% significance level. You need to state the null and alternative hypotheses; report p-value and make a conclusion on it. (10 marks) (c) Find a two-sided 95% confidence interval for . (4 marks) (d) Find a lower 95\% confidence interval for 2. (4 marks) (e) Under 5% significance level, test whether =3. You need to state the null and alternative hypotheses and make a conclusion on it. (10 marks) (32 marks)