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…

"Infidelity According to menstuff.org, 22% of married men have “strayed” at least once during their married lives.

a. Describe how you might go about administering a survey to assess the accuracy of this statement."

"Blind Emotion [See Problem 11 in Section 10.2A.] When the area of the brain responsible for vision is destroyed, individuals experience cortical blindness. Patients with cortical blindness are unaware of any visual stimulus including light. In a 52-year-old male patient with cortical blindness (as a result of two strokes within a 38-day timeframe), a series of visual stimuli were presented on a computer screen. The patient was given two choices for each stimulus and asked to report what was on the screen. The patient’s responses were recorded by an individual who could not see the contents on the screen.

a. An initial baseline test was conducted by presenting black squares and circles on the white background of the screen. The patient correctly “guessed” the item on the screen in 90 of the 200 trials. Researchers concluded the patient’s performance was not statistically different from chance. Explain what this means using the language of hypothesis testing.

"

"Simulation Simulate drawing 100 simple random samples of size n = 40 from a population whose proportion is 0.3.

d. How do we know that a rejection of the null hypothesis results in making a Type I error in this situation?"

True or False: Sample evidence can prove a null hypothesis is true.

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 $p=0.25$

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%.