Homework 1 T-tests

Introduction

The dataset below includes data from the 2014 American Time Use Survey on employed adult males with partners who are also employed. The following variables are included:

• EARNWEEK: weekly earnings

• SPEARNWEEK: partner’s weekly earnings

• UHRSWORKT: usual number of hours worked per week

• SPUSUALHRS: partner’s usual number of hours per week

• EDUCYRS: years of education

• WHITE: binary variable equal to 1.0 if the person is White/Caucasian and 0.0 otherwise

The dataset should be stored in your Rstudio.cloud project files. You can open the dataset with the following cal:

load("timeuse.RData")

This loads the data frame into memory. The data frame object is named, df.

Load the tidyverse library to make use of these functions. If necessary you may need to install the series of packages with a call to install.packages()

# Necessary only one per rstudio.cloud project 
# (So don't put it in your script!)
install.packages("tidyverse")

# Necessary every time you run R 
# (Put it in your script!)
library("tidyverse")

You can view the structure of the data frame with a call to glimpse(), which is available in the tidyverse package.

glimpse(df)

## Observations: 1,063
## Variables: 7
## $ MALE       <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
## $ WHITE      <int> 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,…
## $ EDUCYRS    <int> 16, 15, 18, 16, 14, 16, 12, 19, 18, 0, 12, 14, 12, 15…
## $ UHRSWORKT  <int> 72, 40, 45, 45, 40, 37, 70, 38, 25, 7, 50, 40, 40, 67…
## $ EARNWEEK   <dbl> 800.00, 1000.00, 2884.61, 1538.46, 380.00, 962.00, 62…
## $ SPUSUALHRS <int> 32, 50, 40, 40, 40, 35, 70, 40, 40, 40, 15, 40, 40, 1…
## $ SPEARNWEEK <dbl> 217.50, 1057.69, 2307.69, 961.53, 568.80, 865.00, 617…

Answer the questions below. Type up your answers and submit to the appropriate Canvas assignment folder. Include in your answers (1) the code you used, (2) the output from the code, and (3) your written description of the interpretation of the output as appopriate to answer the question.

Problems

1. Do men on average work a different number hours per week than their partner? Test the appropriate hypothesis. Compute and interpret a 95% confidence interval for the difference between male’s usual weekly hours and their partners’.

2. Do White/Caucasion people have a different average weekly total earnings than non-whites? Test the appropriate hypothesis. Compute and interpret a 95% confidence interval for the difference between average weekly earnings for whites versus non-whites.

3. Is there a relationship between educational attainment and weekly earnings? Test the appropriate hypothesis. Construct and interpret a 95% confidence interval for the appropriate statistic. Comment on the nature of the relationship.

4. Test the hypothesis that employed men work on average more than 40 hours per week. Construct and interpret a 95% confidence interval for the average number of hours that men usually work per week.

5. What other variables in the dataset do you think may affect usual hourly earnings? Describe the relationship you may expect? What statistical tests would you use to determine if these relationships exist?

Submission

Upload your submission to the Canvas assignment folder titled, “Homework 1 - T-tests,” by Monday, February 11, 5:30 PM.

Include in your upload both the .html document and the .Rmd document.