The goal of hypothesis testing is to answer a simple yes / no question about a population parameter. There are two types of hypothesis, $H_{0}$ the null hypothesis and $H_{A}$ the Alternate hypothesis.
The steps followed are:
Rules in hypothesis testing
For a jury trial, our motto is innocent until proven guilty. Hence
$H_{A} => guilty$
Type 1 error: False positive
In practice, we fix $\alpha = 0.5$ and calculate $\beta' = (1-\beta)$
Example
A sample of 49
batteries are tested for their limetimes. The SD is 15.0
, mean longivity is 1006.2
. Is it possible to claim the batteries last longer than 1000
hours on average?
$\bar x = 1006.2$, $n=49$, $s=15$, $\alpha = 0.01$ assumed. $$H_{0} => \mu \le 1000$$ $$H_{A} => \mu > 1000$$
Find Test Statistic $$TS = \frac{1006.2-1000}{15/\sqrt{49}}$$ $$TS=2.89$$ This is a right tailed hypothesis as we test if test statistic is > z score for the said alpha.
z score for $\alpha=0.01$ = 2.576 (for 99% CI) The TS is > z score. Hence reject $H_{0}$. Thus mean battery life > 1000 hours by significance.
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