Fundamental Math

  
Instruction and rules: 
Dear students. In order to have no confusion after the submission, let us set some rules: 
ü Your solutions must be numbered properly. If you do not provide the number of the question you are referring to, you will not receive any credit, even if you have the correct answer! 
ü You can collaborate (whole or partially even in only 1 question), one and ONLY ONE student from your group of collaborators must submit the solutions. Write all the names in the comment section of the submission. Note that you and your collaborates with have a coefficient of 0.8 multiplied by your score on the final exam. If you collaborate (even in 1 question) and not inform me your score will be multiplied by 0 . 
ü For part 2 which is more empirical, I still want your written responses on a paper. Please do not just submit the excel file. Again, your written responses must have numbers referring to the question you are responding to. 
ü Even 1 second of late submission is not accepted. It is not fair to other students. Please follow this rule and do not leave the submission to the last minutes. 
Part 1:
1. Average years of education of individuals in the United States is 13.41 years. The standard deviation is 2.3 years. Bob has 12 years of education. Find what percentage of individuals have less years of education than Bob (assuming the years of education is a Normal variable). 
2. It is believed that average temperature in a normal Winter day is A researcher claims we are experiencing warmer weather during the Winter due to the global warming. She gathers a data set observing 100 normal day in winter and she gets a sample average of The standard deviation she observes is Does this mean she has a statistically significant claim, meaning does her sample rejects or fails to reject (provide both approaches, zscore and pvalue). 
3. The random variable D below takes on the values: 0, 1, 2, 3, 4, 5 ,6 with probabilities: 0.301, 0.202, 0.044, 0.102, 0.055,0.011, 0.285. What is the expected value, variance, and standard deviation of D. 
Part 2:
4. Open the Excel file and carefully read the Data-description. 
5. In the excel file what is the sample mean, sample variance and the standard deviation of variable “ed”. You should report your numbers with appropriate unit of measurement. (For example, if money is it $ or cents?! If age is it years or months?)
6. What is the confidence interval of the sample-mean of “ed”? (Hint: first you should calculate the mean (which you did in part 5), then the margin of error, and then add and subtract the margin of error from the sample mean to find the confidence interval.)
7. Provide a histogram of “bytest”. The bins are your choice. 
8. Provide a scatter plot of “ed” over “dist”. (ed on the vertical and dist on the horizontal axis.) 
9. Do you see any correlation? What is the correlation between ed and dist? Is it positive or negative? What does it mean?
10. Run a regression of ed over dist.  
11. What is the predicted intercept? 
12. What is the predicted slope?
13. What is the effect of dist on ed? (you should read the slope, the slope is the effect of x variable on y, 1 unit of x causes B1 unit of y). 
14. Write down the predicted equation. (you can use excel for this and add the trend line). 
15. What is the predicted value of ed for someone who leaves 30 miles away from the nearest college? (in your predicted equation insert 3 for dist/x and calculate ed/y)
16. What is r-squared of the regression? Is our regression a good fit?
17. Is the B1 significant? Why or why not? 
18. What is the confidence interval for B1? What does this interval mean?