9. Hypothesis Testing for One Sample

Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:

$\alpha =0.01$, $n=40$, $x=28$, & claim is $p=0.75$

Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:

$\alpha =0.10$, $n=100$, $x=42$, & claim is $p=0.25$

A snack company claims that at least 70% of people prefer its new low-sugar granola bar over the original version. To test this claim, a grocery chain surveys a random sample of 80 customers, & 50 say they prefer the new version. Use $\alpha =0.10$ to test whether more than 70% of customers prefer the new granola bar. Should the grocery chain stock more of the new product & reduce shelf space for the original version?

A city government claims that no more than $25\%$ of households have solar panels. A researcher suspects the rate is actually higher and surveys $200$ households, finding that $62$ have solar panels. Test if there is evidence that more than $25\%$ of households have solar panels using $\alpha =0.01$.

$H_0:$_________ $H_a:$_________

$x=$________ $n=$________ $P$-value: ______

Because $P$-value [ < | > ] $\alpha$, we [ REJECT | FAIL TO REJECT ] $H_0$, there is [ ENOUGH | NOT ENOUGH ] evidence to suggest…