Wrong By Design

STAT 20: Introduction to Probability and Statistics

Concept Questions

Instead of constructing a confidence interval to learn about the parameter, we could assert the value of a parameter and see whether it is consistent with the data using a hypothesis test. Say you are interested in testing whether there is a clear majority opinion of support or opposition to the project.


What are the null and alternative hypotheses?

01:00

library(tidyverse)
library(infer)
library(stat20data)

ppk <- ppk |>
  mutate(support_before = Q18_words %in% c("Somewhat support", 
                                          "Strongly support",
                                          "Very strongly support"))

library(tidyverse)
library(infer)
library(stat20data)

ppk <- ppk |>
  mutate(support_before = Q18_words %in% c("Somewhat support", 
                                          "Strongly support",
                                          "Very strongly support"))
obs_stat <- ppk |>
  specify(response = support_before,
          success = "TRUE") |>
  calculate(stat = "prop")

library(tidyverse)
library(infer)
library(stat20data)

ppk <- ppk |>
  mutate(support_before = Q18_words %in% c("Somewhat support", 
                                          "Strongly support",
                                          "Very strongly support"))
obs_stat <- ppk |>
  specify(response = support_before,
          success = "TRUE") |>
  calculate(stat = "prop")
obs_stat
Response: support_before (factor)
# A tibble: 1 × 1
   stat
  <dbl>
1 0.339

null <- ppk |>
  specify(response = support_before,
          success = "TRUE") |>
  hypothesize(null = "point", p = .5) |>
  generate(reps = 500, type = "draw") |>
  calculate(stat = "prop")

null <- ppk |>
  specify(response = support_before,
          success = "TRUE") |>
  hypothesize(null = "point", p = .5) |>
  generate(reps = 500, type = "draw") |>
  calculate(stat = "prop")
null
Response: support_before (factor)
Null Hypothesis: point
# A tibble: 500 × 2
   replicate  stat
   <fct>     <dbl>
 1 1         0.519
 2 2         0.483
 3 3         0.501
 4 4         0.502
 5 5         0.491
 6 6         0.492
 7 7         0.516
 8 8         0.498
 9 9         0.514
10 10        0.489
# ℹ 490 more rows

null <- ppk |>
  specify(response = support_before,
          success = "TRUE") |>
  hypothesize(null = "point", p = .5) |>
  generate(reps = 500, type = "draw") |>
  calculate(stat = "prop")
visualize(null) +
  shade_p_value(obs_stat, direction = "both")

What would a Type I error be in this context?

01:00

What would a Type II error be in this context?