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 = ______
p = 0.2 (since there are five choices and they are randomly guessing)
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
Since ESP means more correct
c). Write down the null and alternative hypotheses for testing whether people have ESP:
H0: p = 0.2
Ha: p > 0.2
where p is the proportion correct for all people’s guesses
since we are looking for evidence that the proportion is significantly
above 0.2 (random guesses)
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?
H0: 1 = 2
Ha: 1  2
where 1 and 2 are the mean words recalled in the two different conditions
since we are looking for evidence that the means are different
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?
H0: pm = pf
Ha: pm  pf
where pm and pf are the proportions supporting gun control for males
and females, respectively
since we are looking for evidence that the proportions are different
b). Is the average hours of sleep per night for college students less than 7?
H0:  = 7
Ha:  < 7
where  is the average number of hours of sleep at night for college students
since we are looking for evidence that the mean is 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?
It means we can conclude that p > 0.2 and that the sample results were so strong that we can
generalize to the population of all guesses that people have ESP and get more right than would be
expected by random chance.
If the results are not statistically significant, what does that mean in terms of ESP?
The sample results are inconclusive. People may or may not have ESP. Sample results could be
just random chance.
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
since it is way bigger than 0.2
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
Since it is even below what we would get just by randomly guessing and gives no evidence that p > 0.2
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?
It means the sample results are so clear that we can generalize to the population and state that
there is a difference between sleep and caffeine in their effectiveness at helping word recall.
If the results are not statistically significant, what does that mean in terms of sleep, caffeine, and
memory?
It means the sample results are inconclusive and we can’t tell if there is a difference.
Results might just be random chance.
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:
H0:  = 100 where  is the average BPA in canned tomatoes
Ha:  > 100
since we are looking for evidence that the mean is greater than 100
Give a possible sample mean that you think would be statistically significant:
x̅ = any value that is quite a bit larger than 100. Make it clear that we are not just determining
whether the sample mean is larger than 100, but are looking for such strong evidence that we can
generalize to the population mean
Give a possible sample mean that would definitely not be statistically significant:
x̅ = any value that is less than 100. If the sample mean is less than 100, it provides no evidence
that the population mean is greater than 100.