3.5 Setting Up a Test for a Population Proportion

Identify an appropriate testing method for a population proportion including the parameter for the population proportion.

• A hypothesis test is a statistical inference procedure that is used to make a decision about the value of a population parameter. The appropriate hypothesis testing procedure is a one-sample z-test for a population proportion.
• The parameter for a hypothesis test for a population proportion should reference the population parameter, the response variable, and the population in context.

Identify the null and alternative hypotheses for a population proportion.

• In the hypothesis testing procedure, the null hypothesis, H0, is the statement about a parameter that is assumed to be correct unless there is convincing statistical evidence suggesting otherwise. It is the status quo condition. The alternative hypothesis, Ha, is the claim or belief about a parameter for which evidence is being collected. A researcher’s claim or belief about the population parameter is represented by the alternative hypothesis.
• The null hypothesis contains an equality reference ,, or . Although the null hypothesis for a one-sided test may include an inequality symbol, in
• The null hypothesis for a one-sample z-test for a population proportion is as follows: H:0 p ,p 0 where p0 is the null hypothesized value for the population proportion. A one-sided alternative hypothesis for a one-sample z-test for a population proportion is either H:a0 pp or H: pp 0a . A two-sided alternative hypothesis is H:a pp 0.

Justify the appropriateness of a hypothesis test for a population proportion by verifying conditions.

• A one-sample z-test for a population proportion requires that three conditions be met:
  • i. The randomization condition—the data should be collected using a random sample.
  • ii. The 10% condition—when sampling without replacement, the population size must be at least 10 times larger than the sample size nN10 , where N is the size of the population and n is the sample size.
  • iii. The normality condition—the expected number of successes, np0 0, and the expected number of failures, n 1 p0 , should be at least 10. Inference for Categorical Data: Proportions UNIT 3 94