Question

question 5
a hospital director believes that 20% of the test tubes in the laboratory are contaminated. however, the healthy magazine published that the number of test tubes is more than 20%.
what are the hypotheses for this test?
$\mathrm{h}_0: p \geq 0.20$ $\mathrm{h}_\mathrm{a}: p < 0.20$
$\mathrm{h}_0: p \leq 0.24$ $\mathrm{h}_\mathrm{a}: p > 0.24$
$\mathrm{h}_0: p = 0.00$ $\mathrm{h}_\mathrm{a}: p \
eq 0.00$
$\mathrm{h}_0: \mathrm{p} = 0.20$ $\mathrm{h}_\mathrm{a}: p > 0.20$

Explanation:

The null hypothesis ($H_0$) is the initial claim, here the hospital director believes 20% (0.20) of test tubes are contaminated, so $H_0: p = 0.20$. The alternative hypothesis ($H_a$) is what the magazine claims, that the proportion is more than 20%, so $H_a: p > 0.20$. We check the options: the first has $H_a$ as less, second has wrong proportion (0.24), third is unrelated, fourth matches.

Answer:

D. $\boldsymbol{\mathrm{H}_0: p = 0.20\quad \mathrm{H}_a: p > 0.20}$ (assuming the last option is D; if options are labeled as per the order, the last option with $H_0: p = 0.20$ and $H_a: p > 0.20$)