In NUstat/ISDStutorials: Tutorial Lessons for Introduction to Statistics and Data Science

library(learnr)
library(tidyverse)
library(tutorialExtras)
library(gradethis)

gradethis_setup()
knitr::opts_chunk$set(echo = FALSE)

grade_server("grade")

question_text("Name:",
              answer_fn(function(value){
                              if(length(value) >= 1 ) {
                                return(mark_as(TRUE))
                                }
                              return(mark_as(FALSE) )
                              }),
              correct = "submitted",
              allow_retry = FALSE )

grade_button_ui(id = "grade")

Instructions

Complete this tutorial while reading Sections 9.0 - 9.1 of the textbook. Each question allows 3 'free' attempts. After the third attempt a 10% deduction occurs per attempt.

You can click the "View Grade" button as many times as you would like to see your current grade and the number of attempts you are on. Before submitting make sure your grade is as expected.

Goals

• Understand the Normal distribution, T-distribution and Chi-squared distribution, and when to employ each.
• Describe modality and skewness of a distribution.
• Understand and know when to apply the Empirical Rule.

Reading Quiz

quiz(
  caption = NULL,
  #Question 1
  question("Q1) Which of the following are TRUE about the Normal distribution? Select all that apply.",
           answer("It is symmetric", correct = TRUE),
           answer("It is unimodal", correct = TRUE),
           answer("It will always be centered at 0"),
           answer("It is characterized by two parameters:  $\\mu$ and $\\sigma$", correct = TRUE),
           answer("The shape depends on the degrees of freedom"),
           allow_retry = TRUE,
           random_answer_order = TRUE),
  # Question 2
  question_blank(paste0("<strong> Q2) Consider the plot of two Normal distributions.</strong> <br/>",  htmltools::img(src="images/norm_dist_dashed.png", height = 500, width = 650), " <br/>
  a) What is the value of ($\\mu$) for the solid line curve? ___  <br/>
  b) What is the value of ($\\mu$) for the dashed line curve? ___  <br/>
  c) Which curve has the larger standard deviation ($\\sigma$)? (Specify either solid or dashed) ___" ),
           answer("100", correct = TRUE),
           answer("100", correct = TRUE),
           answer("dashed", correct = TRUE),
           allow_retry = TRUE),
 # Question 3
  question_blank(paste0("<strong> Q3) The distribution of number of hours spent studying a week is normally distributed with a mean of 5 hours and a standard deviation of 1 hour. Based on the empirical rule...</strong> <br/>

a) 68% of students spend between ___ and ___ hours studying. 
<br/>
b) ___ % of students spend between 3 and 7 hours studying. 
<br/>
c) 99.7% of students spend between ___ and ___ hours studying"),
           answer_fn(function(value){
                    if(value %in% c(4, "four")){return(mark_as(TRUE))}
                       return(mark_as(FALSE) )}),
           answer_fn(function(value){
                    if(value %in% c(6, "six")){return(mark_as(TRUE))}
                       return(mark_as(FALSE) )}),
           answer("95", correct = TRUE),
           answer_fn(function(value){
                    if(value %in% c(2, "two")){return(mark_as(TRUE))}
                       return(mark_as(FALSE) )}),
           answer_fn(function(value){
                    if(value %in% c(8, "eight")){return(mark_as(TRUE))}
                       return(mark_as(FALSE) )}),
           allow_retry = TRUE),
#Q4
  question_wordbank("Q4) True or False?: Determine if the following QQ plots indicate that the data is normally distributed.",
           choices = c(paste0(htmltools::img(src="images/qqplot_2.png", height = 200, width = 350) ), paste0(htmltools::img(src="images/qqplot_1.png", height = 200, width = 350) ), paste0(htmltools::img(src="images/qqplot_3.png", height = 200, width = 350) ) ),
           wordbank = c("True", "False"),
           answer(c("False", "True", "False"),correct=TRUE),
           allow_retry = TRUE),
  # Q5
  question_numeric("Q5) The annual salaries of students after graduation follow a normal distribution with a mean of $50,000 and a standard deviation of $10,000.

Compute the STAT of the value x = $35,000.", 
           answer(-1.5, correct = TRUE),
           allow_retry = TRUE),
  # Q6
  question_wordbank("Q6) Consider a standardized statistic that follows a standard normal distribution. Match each of the following values with where you would expect them to fall on the standard N(0,1) distribution.",
        choices = c("0.73", "2.6", "0", "-1.3", "-3.4"),
        wordbank = c("somewhat to the right of center","far right tail", "center", "somewhat to the left of center", "far left tail"),
        answer(c("somewhat to the right of center","far right tail", "center", "somewhat to the left of center", "far left tail"), correct = TRUE), 
        allow_retry = TRUE ),
  # Q7
  question("Q7) The annual salaries of students after graduation follow a normal distribution with a mean of $50,000 and a standard deviation of $10,000.

Which of the following will calculate the probability that a person makes *less than* $55,000 after graduating? Select all that apply.  ",
           answer("qnorm(p=55000, mu=50000, sd=10000)"),
           answer("pnorm(q=0.5, mu=0, sd=1)", correct = TRUE),
           answer("pnorm(q=0.5, mu=50000, sd=10000)"),
           answer("pnorm(q=55000, mu=50000, sd=10000, lower.tail=FALSE)"),
           answer("pnorm(q=55000, mu=50000, sd=10000)", correct = TRUE),
           allow_retry = TRUE,
           random_answer_order = TRUE),
  # Q8
  question("Q8) What does the parameter 'df' stand for? ", 
           type = "learnr_text",
           answer_fn(function(value){
             if (str_remove_all(str_to_lower(value), " ") %in% c("degreesoffreedom") ) {
               return(mark_as(TRUE))
               }
             return(mark_as(FALSE) )
             }),
           allow_retry = TRUE),
  # Q9
  question("Q9) Which of the following are TRUE about the t-distribution? Select all that apply.  ",
           answer("It has heavier tails than the Normal distribution", correct = TRUE),
           answer("It is symmetric", correct = TRUE),
           answer("It is characterized by two parameters: $\\mu$ and $\\sigma$"),
           answer("It is bimodal"),
           answer("The thickness (or 'heaviness') of the tails depends on the sample size", correct = TRUE),
           allow_retry = TRUE,
           random_answer_order = TRUE)

)

Submit

Once you are finished:

• Click the 'Download Grade' button below. This will download an html document of your grade summary.
• Make sure your grade is correct and as expected!
• Submit the downloaded html to Canvas.

grade_print_ui("grade")

NUstat/ISDStutorials documentation built on April 17, 2025, 6:15 p.m.