# Does a conjecture show that a statement is false?

## Does a conjecture show that a statement is false?

If a conjecture is made, and can be determined that it is false, it takes only one false example to show that a conjecture is not true. The false example is called a counterexample.

### Which statement is a conjecture?

A statement that might be true (based on some research or reasoning), but is not proven. Like a hypothesis, but not stated in as formal, or testable, way. So a conjecture is like an educated guess.

#### What is a conjecture or conclusion?

In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found.

Why it only takes one counterexample to prove that a conjecture is false?

Only one counterexample is necessary to show that a conjecture is false because for a conjecture to be true, it must be true for ALL situations/cases.

When do we make a conclusion from a statistical test?

When we make a conclusion from a statistical test there are two types of errors that we could make. They are called: Type I and Type II Errors Type I error –reject H 0 when H 0 is true. Type II error –do not reject H 0 when H 0 is false. Results of a statistical test: i Error H 0 s True s False Reject

## How are null and alternative hypotheses stated together?

The null and alternative hypotheses are stated together. T H 0 he following are typical hypothesis for means, where kis a specified number. CH8: Hypothesis Testing Santorico – Page 273

### When to reject a null hypothesis in two tailed test?

Two-tailed test – the null hypothesis should be rejected when the test value is in either of two critical regions on either side of the distribution of the test value. To obtain the critical value, the researcher must choose the significance level, , and know the distribution of the test value.

#### How does the decision of the jury prove something?

 The decision of the jury does not prove that the defendant did or did not commit the crime.  The decision is based on the evidence presented.  If the evidence is strong enough the defendant will be convicted in most cases, if it is weak the defendant will be acquitted.  So the decision to reject the null hypothesis does not prove anything.