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?
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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
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
What would a Type I error be in this context?
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What would a Type II error be in this context?