Stating hypotheses

About this lesson

Statistics (AP-aligned) › Significance tests

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Stating hypotheses

Warm-up

Three quick questions from earlier lessons.

Discover

A courtroom presumes innocence until the evidence is convincing. In a significance test, which hypothesis plays the role of "innocent"?

  1. The null hypothesis H₀
  2. The alternative Hₐ

Key idea

State the question as two hypotheses about a parameter.

H₀ (null): the parameter equals a specific value (no effect). Hₐ (alternative): what we look for evidence of: <<, >> (one-sided) or ≠\ne (two-sided). Hypotheses are about parameters (pp, μ\mu), never statistics.

Worked example

A factory says bulbs last 1,000 hours on average; a buyer suspects less.

H0:μ=1000H_0: \mu = 1000
Status quo.
Ha:μ<1000H_a: \mu < 1000
The suspicion.
One-sided test
Direction given.

Your turn, guided

Your turn: in "H₀: p = 0.3, Hₐ: p ≠ 0.3", what is the null value p0p_0?

p0=0.3p_0 = 0.3
The value in H₀.

Practice ★

  1. A company claims that 80% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
    1. H₀: p = 0.80
    2. H₀: p < 0.80
    3. H₀: p̂ = 0.80
  1. The mean wait at a clinic used to be 81 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
    1. Hₐ: μ ≠ 81
    2. Hₐ: μ > 81
    3. Hₐ: x̄ ≠ 81

Watch out!

Practice ★★

  1. Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 445)?
    1. Because we know p̂ exactly; the question is about the unknown population value
    2. Because statistics are harder to compute
    3. There is no difference between p and p̂

Exit ticket

Three questions to check you have got it.

  1. A company claims that 80% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
    1. H₀: p = 0.80
    2. H₀: p < 0.80
    3. H₀: p̂ = 0.80
  2. A company claims that 60% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
    1. H₀: p = 0.60
    2. H₀: p < 0.60
    3. H₀: p̂ = 0.60
  3. A company claims that 62% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
    1. H₀: p = 0.62
    2. H₀: p < 0.62
    3. H₀: p̂ = 0.62

Summary card

Hypotheses

H₀: parameter = value. Hₐ: <, >, or ≠.

Watch out: parameters, never statistics.

End of the lesson

Next lesson: The one-proportion z test and P-values Back to the chapter

Answers: Stating hypotheses

A

  1. H₀: p = 0.80

B

  1. Hₐ: μ ≠ 81

C

  1. Because we know p̂ exactly; the question is about the unknown population value

D

  1. H₀: p = 0.80
  2. H₀: p = 0.60
  3. H₀: p = 0.62

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