This dataset contains 200 observations randomly sampled from the High School and beyond Survey, a survey conducted on high school seniors by the NationalCenter of Education Statistics. For the details of the variables please refer to the following link:https://www.openintro.org/data/index.php?data=hsb2

(1) Some past research suggested that high school seniors do equally well in reading and writing. As high school teachers we believe that students nowadays are better at reading than writing under the influence of new technologies. According to the above information, use the "read"and "write" variables in the dataset to conduct the following analysis. (Hint:two sample t test)

(a) State your null and alternative hypotheses

(b) Test your hypotheses and state your conclusion

(2) We would like to study how students from different racial and socio-economic backgrounds perform on math tests with a linear regression. The dependent variable for this analysis should be "math" and the independent variables for this analysis should be "race" and "ses"(socio-economic status of students' family).

(a) Check whether the two independent variables "race" and "ses" are factor variables. If not, create corresponding factor variables for our linear regression analysis.

(b) Run a linear regression where y is math score and x's are factor variables of race and socio-economic status. With a significance level of 5% which variables are significant?

(c) Use a function to show the dummy structure of race and socio-economic status factors respectively. What are the baselines for race and socio-economic status respectively? When other factors are held constant, what is the average math score difference between an Asian student and a white student?

(d) What is the average math score for a student that is of Hispanic background and from a family of middle socio-economic status?

(3) This article (https://www.guitarworld.com/news/90-percent-of-new-guitarists-abandon-the-instrument-within-a-year-according-to-fender)suggests that 90% of new guitarists abandon the instrument within a year according to Fender (an American guitar manufacturer). We run a local guitar shop. From our own experience, we speculate that this number is not correct. We conducted an online survey and interviewed 150 randomly selected guitarists and found that 133 out of 150 guitarists gave up playing guitar within the first year. According to the above information,

(a) Set up your null and alternative hypotheses

(b) Test your hypotheses with a one sample proportion test and state your conclusion