Hand Coding the Power of a Test

We want to test if our population average is different from twenty.

We therefore specify the follow zero hypothesis.

$$ H_0: \mu = 20 $$

The alternative hypothesis is

$$ H_a: \mu \neq 20 $$

Accepting

{% highlight r %} mu <- 40 sd <- 8 n <- 20 ci <- qnorm(0.975)*sd/sqrt(n) (left <- mu - ci) {% endhighlight %}

{% highlight text %}

[1] 36.49391

{% endhighlight %}

{% highlight r %} (right <- mu + ci) {% endhighlight %}

{% highlight text %}

[1] 43.50609

{% endhighlight %}