Question

a researcher claims that less than 25% of american adults are allergic to pollen. in a random sample of 100 adults, 20% indicate that they have such an allergy. Calculate the test statistic z for the population portion.

Answer 1

ANSWER

Z = -1.25

EXPLANATION

Given:

$Hypotheses=\begin{cases}{H_0:p\text{ = 0.25}} \\ {H_a:p<0.25} \\ {}\end{cases}$

Desired Outcome:

Test Statistic z

Determine the Test Statistic z

$z\text{ = }\frac{p\text{ - p}_0}{\sqrt{\frac{p_0(1\text{ - p}_0)}{n}}}$$\begin{gathered} z\text{ = }\frac{0.20-0.25}{\sqrt{\frac{0.25(1\text{ - 0.25\rparen}}{100}}} \\ z\text{ = }\frac{-0.05}{\sqrt{\frac{0.1875}{100}}} \\ z\text{ = }\frac{-0.05}{0.04} \\ z\text{ = -1.25} \end{gathered}$