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Problem 1. To see if there is any significant difference between the average mortgages in the southern (referred to as population 1) and the northern California (referred to as population 2), the following information was gathered. South (1) North (2) Sample Size 40 45 Sample Mean (in $1000) $170 $175 Sample Standard Deviation (in $1000) $5 $7 Please answer the following questions (question 1.1 to question 1.10) regarding problem 1 (for dollar value, please use $1000 as unit, i.e., in all your calculation, please directly use the numbers listed in the above table) Question 1.1. The sample mean difference in problem 1 follows which of the following probability distribution? O t distribution O Normal distribution O Binomial distribution O Standard normal distributionD Question 2 Question 1.2. What is the standard deviation (standard error) of sample mean difference in problem 1? (use $1000 as unit, i.e., the numbers directly from the D Question 3 Question 1.3. What should be the Null hypothesis for problem 1? Ou1 =_2 Oulzu2 OH1 21 2 Ou1su_2 D Question 4 Question 1.4. What should be the Alternative hypothesis for problem 1? Ou_1 + H_2 Ou1 = H_2 Ou1zu_2 Oulsu2Question 5 Question 15. What is the degree of freedom of the distribution for sample mean difference in problem 1? Question 6 Question 1.61 What are the test statistics for problem 1? {include sign of the number) Question 7 Question 1.71 What is the p-value of the test statistics for problem 1? Question 8 Question 13' if (1 = 0.05 is used, what is the critical value? (for multiple values, enter the positive one]