Hypothesis Testing Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
State null and alternative hypotheses for each scenario: (a) testing if a coin is fair, (b) testing if a new drug reduces fever faster than the standard drug.

Solution

  1. 1
    (a) Coin: H0:p=0.5H_0: p = 0.5 (fair coin); Ha:pโ‰ 0.5H_a: p \neq 0.5 (biased; two-tailed)
  2. 2
    (b) Drug: H0:ฮผnew=ฮผstandardH_0: \mu_{\text{new}} = \mu_{\text{standard}} (no difference); Ha:ฮผnew<ฮผstandardH_a: \mu_{\text{new}} < \mu_{\text{standard}} (new drug reduces fever faster; one-tailed)

Answer

(a) H0:p=0.5H_0: p=0.5; Ha:pโ‰ 0.5H_a: p \neq 0.5. (b) H0:ฮผN=ฮผSH_0: \mu_N = \mu_S; Ha:ฮผN<ฮผSH_a: \mu_N < \mu_S.
Hypotheses must be stated before seeing data. Hโ‚€ is always the default/status-quo claim; Hโ‚ is the research hypothesis. The choice of one-tailed vs. two-tailed depends on whether we expect a specific direction of difference.

About Hypothesis Testing

A systematic method to decide whether sample data provides enough evidence to reject a claim (null hypothesis) about a population parameter.

Learn more about Hypothesis Testing โ†’

More Hypothesis Testing Examples

Example 1 medium

A school claims its students average 75 on standardized tests. A sample of [formula] gives [formula]

Example 2 hard

A medication is claimed to reduce blood pressure by 10 mmHg on average. A clinical trial with [formu

Example 4 hard

A teacher claims students average 80 points. A skeptic samples [formula] students: [formula], [formu

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