ECO 321 Fall 2020

Homework 1

Due September 4 by 5 pm

Cut and paste at the end of your submission the R code you have used in problem 2 to show your work.

1. Suppose in a survey of n = 1000 students, 600 responded that they prefer small classes and 400 responded that they prefer large classes. Let p denote the fraction of all students who preferred small classes at the time of the survey, and X be the fraction of survey respondents who preferred small classes. (Hint: X is distributed as a Bernoulli random variable)
2. (a)Show that E(X ) = p and Var(X ) = p(1 p)/n.
3. (b)Use the survey result to estimate p, and calculate the standard error of your
4. estimator. (Hint: Notice that this is the same as estimating the sample mean)
5. On Blackboard under the Homework1 folder, you can find a zip file birthweight.zip which contains a database birthweight smoking.csv for birth weight of infant (in grams) with an indicator equal to one if the mother smoked during pregnancy and zero, otherwise. A detailed description is given in the pdf file Data description. you will investigate the the relationship between a mother smoked during pregnancy (smoker) and birth weight of infant (birthweight). smoker takes value 1 is the mother smoked during pregnancy and 0 otherwise. (Hint: If you are looking for general methods to save plots in R, please look at the following webpage http://www.sthda.com/english/wiki/creating-and-saving-graphs-r-base-graphs. Do not use "Export" command )
6. (a)Load the dataset into R and call it data weight. What command did you use? (Do not use the "import dataset" command in Rstudio.)
7. (b)How many observations are there in your sample? How many variables?
8. (c)Rename the variable birthweight to brght
9. (d)Report the min, max and quartiles of brght.
10. (e) a histogram for brght with density for Y-Axis instead of frequency.
11. (f)Report the mean, standard deviation and skewness of brght. Would you say that this variable is normally distributed based on the value of skewness?