A local park claims that less than 15% of visitors litter. A random sample of 120 visitors finds that 25 litter. At the 0.05 significance level, test if the proportion of visitors who litter is greater than 15%.

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…

A city claims that $30\%$ of households recycle regularly. A researcher surveys $200$ households to see if the true proportion is different and finds that $78$ recycle regularly. Use $\alpha =0.05$ to test the claim.

$H_0:$_________ $H_a:$_________

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

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

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 $p=0.25$

Feeling Your Age A research organization conducts a survey by randomly selecting adults and asking each, “How do you feel relative to your age?” The results are shown in the figure. (Adapted from Pew Research Center)

[IMAGE]

a. Use a sign test to test the null hypothesis that the proportion of adults who feel older is equal to the proportion of adults who feel younger. Assign a + sign to each adult who responded “older,” assign a - sign to each adult who responded “younger,” and assign a 0 to each adult who responded “my age.” Use α = 0.05

Contacting Parents A research organization conducts a survey by randomly selecting adults and asking each, “How frequently do you contact your parents by phone?” The results are shown in the figure. (Adapted from Pew Research Center)

a. Use a sign test to test the null hypothesis that the proportion of adults who contact their parents by phone weekly is equal to the proportion of adults who contact their parents by phone daily. Assign a + sign to each adult who responded “weekly,” assign a - sign to each adult who responded “daily,” and assign a 0 to each adult who responded “other.” Use α = 0.05

Explain how to test a population proportion p.

In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.

Claim: p <0.12, α=0.01. Sample statistics: p_hat = 0.10, n=40