Proving claims

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Intros

Lessons

$\cdot$ Disprove $H_0$ $\Rightarrow$ Proves $H_1$
$\cdot$ Fail to Disprove $H_0$ $\Rightarrow$ Nothing!

$\cdot$ It is impossible to prove $H_0$ true, nor is it possible to disprove $H_1$ .
$\cdot$ If your claim is given in the form of $H_1$ it may be possible to prove it

Examples

Lessons

Consequences of Disproving $H_0$
Let the Null Hypothesis be given as: $H_0: \mu =17lbs$ $H_{0} : μ = 17 l b s$ ;
and the Alternative Hypothesis be: $H_1: \mu$ $H_{1} : μ$ < $17lbs$ $17 l b s$
If the Null Hypothesis is proven to be false, then what can be said about the mean weight?
The following claim is made. "More than 80% of fortune tellers are frauds".
1. State the Null Hypothesis and the Alternative Hypothesis.
2. If enough evidence is gathered to disprove the Null Hypothesis, then what can be said about the proportion of fraudulent fortune tellers?
3. If there is not enough evidence to disprove the Null Hypothesis, then what can be said about the proportion of fraudulent fortune tellers?

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