Section 4.1: Introducing Hypothesis Tests
Example 1: Extrasensory Perception (ESP)
In an ESP test, one person writes down one of the letters A, B, C, D, or E and tries to telepathically
communicate the choice to a partner. The partner then tries to guess what letter was selected. If there
is no ESP and people are just randomly guessing from among the five choices, what proportion of
guesses would be correct?
a). If no ESP, we expect p = ______
b). Which sample proportion correct would provide the greatest evidence that people have ESP:
(If we assume the sample size is the same in every case.)
𝑝̂ = 0.1
𝑝̂ = 0.25
𝑝̂ = 0.4
𝑝̂ = 0.7
c). Write down the null and alternative hypotheses for testing whether people have ESP:
Example 2: Sleep vs Caffeine for Memory
In an experiment, students were given words to memorize, then were randomly assigned to either take
a 90 minute nap or take a caffeine pill. A couple hours later, they were tested on their recall ability. We
wish to test to see if the sample provides evidence that there is a difference in mean number of words
people can recall depending on whether they take a nap or have some caffeine.
What are the null and alternative hypotheses for this test?
Quick Self-Quiz: Writing hypotheses
Write down the hypotheses for the test in each case below:
a). Does the proportion of people who support gun control differ between males and females?
b). Is the average hours of sleep per night for college students less than 7?
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Example 1 Revisited: Statistical Significance and ESP
If the results of a test for ESP are statistically significant, what does that mean in terms of ESP?
If the results are not statistically significant, what does that mean in terms of ESP?
Which sample proportion correct is most likely to show statistical significance? (If we assume
the sample size is the same in every case.)
𝑝̂ = 0.1
𝑝̂ = 0.25
𝑝̂ = 0.4
𝑝̂ = 0.7
Which sample proportion correct is least likely to show statistical significance? (If we assume
the sample size is the same in every case.)
𝑝̂ = 0.1
𝑝̂ = 0.25
𝑝̂ = 0.4
𝑝̂ = 0.7
Example 2 Revisited: Statistical Significance for Sleep vs Caffeine
If the results of the test comparing sleep and caffeine for memory are statistically significant,
what does that mean in terms of sleep, caffeine, and memory?
If the results are not statistically significant, what does that mean in terms of sleep, caffeine, and
memory?
Quick Self-Quiz: Statistical Significance
A sample of 50 cans of tomatoes are tested for levels of the chemical BPA to see if there is evidence that
the mean level is greater than 100 ppb (parts per billion).
Write down the hypotheses for this test:
Give a possible sample mean that you think would be statistically significant:
Give a possible sample mean that would definitely not be statistically significant: