Can you show steps, please?

Homework 10 questions are given below: (1) Oncologists wanted to know the effect of sex (male, female) on age at diagnosis of colorectal cancer. They extracted a random sample of 30 medical charts of colorectal cancer patients and recorded the sex and age of each patient. These oncologists collaborated with a statistician to fit a simple linear regression model to these data. a. Name the variables in this model? b. For each variable, say what type of variable it is (for example, categorical or continuous). C. Using notations (such as Y for outcome, X1 for predictor, beta0, betal etc for slope, intercept etc), write down the regression model, defining all terms. d. Suppose the statistician uses the following code for sex in the regression model: X1 = 1 for males and X1 = 0 for females. Suppose the intercept is estimated to be 60 and the slope of the regression is estimated to be 5. Interpret the slope. e. Suppose the statistician fits a linear regression to the data extracted by these oncologists and wants to test whether the association between sex and age at diagnosis of colorectal cancer is O. i. What is the sampling distribution of the test statistic? ii. What is the degrees of freedom, if any, of this sampling distribution? Give BOTH the formula and the number based on the statement of the problem. f. As given in problem 4 above, the slope is estimated to be 5. Suppose the standard error of the slope is 1. Conduct a hypothesis test to test whether there is an association between sex and age at diagnosis of colorectal cancer. [0.5 point: 0.05 point for specifying type | error, 0.05 point for writing HO and HA, 0.1 point for calculating the correct test statistic. 0.1 point for giving the correct critical value. 0.1 point for giving the correct decision. 0.1 point for writing the correct scientific conclusion