14.8 Intro to Inferential Statistics

The goal of inferential statistics is to infer information about an entire population by examining a random sample from that population.

%%Testing a Claim about a Population Proportion Intuitively%%

• In statistics a hypothesis is a statement or claim about a property of an entire population.
  • In this section we study hypotheses about the true proportion p of individuals in the population with a particular characteristic.
  • Suppose that individuals having a particular property are assumed to form a proportion p0 of a population. To answer the question of how this assumption compares to the true proportion p of these individuals, we begin by stating two opposing hypotheses.
• The null hypothesis, denoted by H0, states the “assumed state of affairs” and is expressed as an equality: p=p0  
• The alternative hypothesis (also called the research hypothesis), denoted by H1, is the proposed substitute to the null hypothesis and is expressed as an inequality: p>p0, or p

%%Testing a Claim about a Population Proportion Using Probability: The -Value%%

• A “very small” P-value tells us that it is “very unlikely” that the sample we got was obtained by chance alone, so we should reject the null hypothesis.
• The P-value at which we decide to reject the null hypothesis is called the significance level of the test and is denoted by alpha (α).

Testing a Hypothesis

1. Formulate the Hypotheses. First state a null hypothesis and an alternative hypothesis.
2. Obtain a Random Sample. Obtain a sample that is selected arbitrarily and without bias.
3. Calculate the P-Value. Use a calculator to find the p-value associated with the sample obtained.
4. Make a Conclusion. A p-value smaller than the significance level of the test indicates that we should reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

%%Inference about Two Properties%%

• Most statistical studies involve a comparison of two groups, usually called the treatment group and the control group.
  • For example, when researchers are testing the effectiveness of an investigational medication, two groups of patients are selected.
  • The individuals in the treatment group are given the medication; the individuals in the control group are not. The proportions of patients who recover in each group is compared.
  • The goal of the study is to determine whether the difference in the proportion that recovers is statistically significant (and not just the result of chance alone).

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