For each of the following questions of interest formally state the null and alternative hypotheses using symbols.
Are children exposed to pesticides more likely to develop ADHD (attention-deficit/hyperactivity disorder) than those who aren’t exposed?
Is the average age of ICU patients at this hospital greater than 50 years?
If you want to remember something, does taking a nap work better than having some caffeine?
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Are children exposed to pesticides more likely to develop ADHD (attention-deficit/hyperactivity disorder) than those who aren’t exposed?
\[
H_0: p_{\text{exposed}} = p_{\text{not exposed}} \\
H_1: p_{\text{exposed}} > p_{\text{not exposed}}
\]
where \(p\) is the proportion of
children diagnosed with ADHD.
Alternatively,
\[ H_0: p_{\text{exposed}} - p_{\text{not exposed}} = 0 \\ H_1: p_{\text{exposed}} - p_{\text{not exposed}} > 0 \]
Is the average age of ICU patients at this hospital greater than 50 years?
\[
H_0 : \mu = 50 \\
H_1 : \mu > 50
\]
where \(\mu\) is the population mean
age (in years) in the hospital’s ICU unit.
If you want to remember something, does taking a nap work better than having some caffeine?
\[
H_0 : \mu_{\text{nap}} = \mu_{\text{caffeine}} \\
H_1 : \mu_{\text{nap}} > \mu_{\text{caffeine}}
\]
where \(\mu\) is the average number of
items remembered from a list (that the researcher has developed and used
for testing the participants).
Alternatively:
\[ H_0 : \mu_{\text{nap}} - \mu_{\text{caffeine}} = 0\\ H_1 : \mu_{\text{nap}} - \mu_{\text{caffeine}} > 0 \]