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.

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

*p*0 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<0,*or*p*≠*p0*.The P-value is the probability that the difference between the proportions in the two samples is due to chance alone. So if the P-value is small (less than the significance level of the test), we reject the null hypothesis.

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).

**Formulate the Hypotheses.**First state a null hypothesis and an alternative hypothesis.**Obtain a Random Sample.**Obtain a sample that is selected arbitrarily and without bias.**Calculate the****P-Value.**Use a calculator to find the p-value associated with the sample obtained.**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.

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).

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

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

*p*0 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<0,*or*p*≠*p0*.The P-value is the probability that the difference between the proportions in the two samples is due to chance alone. So if the P-value is small (less than the significance level of the test), we reject the null hypothesis.

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).

**Formulate the Hypotheses.**First state a null hypothesis and an alternative hypothesis.**Obtain a Random Sample.**Obtain a sample that is selected arbitrarily and without bias.**Calculate the****P-Value.**Use a calculator to find the p-value associated with the sample obtained.**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.

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).