Cogito
AP Statistics · Chapter 3 · Lesson 2
Significance Tests for a Proportion
Deciding whether a claim survives the data.
12 problems · about 22 minutes · VAR-6.E, DAT-3.A
What this lesson teaches
The student carries out a one-sample z-test for a proportion with full justification.
- State hypotheses about the population proportion.
- Check random, independence and large-sample conditions using p₀.
- Compare the p-value to alpha and conclude in context.
Warm Up
Straightforward practice. Get the method working first.
5 problemsSample 0.55, p₀ = 0.5, standard error 0.05. What is z?
Answer 1
Why 1.
Which proportion is used to compute the standard error in a test?
Answer The null value p₀.
Why p₀, because the null is assumed while testing.
p₀ = 0.5, n = 400. Standard error?
Answer 0.025
Why √(0.25 ÷ 400).
p₀ = 0.5, n = 100. What is np₀?
Answer 50
Why 100 × 0.5.
Both np₀ and n(1−p₀) must be at least what number?
Answer 10
Why The large-sample condition.
Build It Up
The same ideas with more to keep track of.
3 problemsSample 0.6, p₀ = 0.5, standard error 0.05. What is z?
Answer 2
Why 0.1 ÷ 0.05.
p-value 0.016 at alpha 0.05. Reject the null? 1 yes, 0 no.
Answer 1
Why Below alpha.
Should hypotheses be about the parameter or the statistic? 1 parameter, 2 statistic.
Answer 1
Why The population value.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsPut the test procedure in order.
Answer 1. State hypotheses about the population proportion. 2. Check the random, independence and large-sample conditions. 3. Compute the test statistic and the p-value. 4. Compare to alpha and conclude in context.
Why Conditions are checked before any computation.
p₀ = 0.5, n = 2500. Standard error?
Answer 0.01
Why √(0.25 ÷ 2500).
The Standard Error: p₀ = 0.5 and n = 100. What is the standard error?
Answer 0.05
Why 0.05.
The Statistic: Sample proportion 0.62, p₀ = 0.5, standard error 0.05. What is z?
Answer 2.4
Why 2.4.