The Hypothesis Testing Method
Write H0: population parameter = _____
Ha: population parameter <, > or ≠ _____
Collect data
Calculate the sample statistic that estimates population parameter
Is the sample statistic consistent with Ha?
YES
NO
Is the P-value small enough to doubt H0?
NO
(Although the sample statistic
supports Ha that’s not enough,
because there is a reasonable
chance that it’s the result of random
fluctuation in the sample data.)
So…
The sample data is not unusual enough
to give significant evidence against H0,
so we continue to assume H0 true.
YES
The P-value is less than
.10/.05/.01/.001, so there
is some/fairly strong/very
strong/extremely strong
evidence for Ha and
against H0
So…
The sample data is unusual enough to
give significant evidence against H0.
So the data gives significant support
for Ha.
By Read Vanderbilt, 2019
How to Find the P-value
Hypothesis Tests for 1 or 2 Population Proportions
Categorical Data
Using Simulation to do a 1-population proportion hypothesis test (Chapter 11)
1. If a graph isn’t given: Run a simulation 1,000 or 10,000 times, assuming the null is true. Use the
Rossman Chance 1 Proportion applet
̂ ) on the dot plot
2. Find your study’s sample proportion (𝒑
3. Count up the number of simulations as extreme or more extreme than your sample proportion. In
̂ to the end of the tail
other words, count the number of simulations from 𝒑
➢ Tip: You can use the Number of Heads ≤ or ≥ function, on the left side of the applet
4. If it’s a two-tail test: multiply that total times 2 to find the number of simulations in both tails.
5. Divide by the total number of simulations to turn the total number of simulations into a
proportion. That’s your p-value!!
Using the Normal Calculator (Chapter 13)
1. Identify the mean: Assume H0 is true – so the mean of your normal distribution is the number given
in the null hypothesis (H0)
2. Find the standard deviation
a. One population test: standard deviation =
b. Two population test: standard deviation = 𝑆𝐸𝑝̂1−𝑝̂2 =
3. Use the StatCrunch normal calculator (Stat → Calculators → Normal) to find the area from your
study’s sample proportion or difference of proportions to the end of the tail.
4. If it’s a two-tail test: multiply that area times 2
Using StatCrunch Tests (Chapters 16-17)
1. Select the test
a. For a test involving a single proportion 𝑝̂: Stat → Proportion Stats → One Sample
b. For a test involving a two proportions 𝑝̂1 and 𝑝̂2: Stat → Proportion Stats → Two Sample
2. Choose With Summary unless you are given the raw data
3. Number of observations is the sample size, n
4. Number of successes may be given. If not calculate it by multiplying the proportion(s) given in the
question times n. In other words, calculate 𝑥 = 𝑛 ∙ 𝑝̂
5. Click the hypothesis test button and describe the hypotheses
6. Ask for a P-value plot
7. Click Calculate