a medical researcher says that less than 80% of adults in a certain country think that healthy children should be required to be vaccinated. in a random sample of 600 adults in that country, 78% think that healthy children should be required to be vaccinated. at $ \alpha = 0.01 $, is there enough evidence to support the researchers claim? complete parts (a) through (d) below. adult in the country who thinks that healthy children should be required to be vaccinated. state $ h _ { 0 } $ and $ h _ { a } $. select the correct choice below and fill in the answer boxes to complete your choice (round to two decimal places as needed.) $ \bigcirc \mathrm { a } $ $ h _ { 0 } : p \leq $ $ h _ { a } : p $ $ \bigcirc \mathrm { b } $ $ h _ { 0 } : p $ $ h _ { a } : p \leq $ $ \bigcirc \mathrm { e } $ $ h _ { 0 } : p \ eq $ $ h _ { a } : p = $ $ \bigcirc \mathrm { f } $ $ h _ { 0 } : p \geq 0.80 $ $ h _ { a } : p

Question

a medical researcher says that less than 80% of adults in a certain country think that healthy children should be required to be vaccinated. in a random sample of 600 adults in that country, 78% think that healthy children should be required to be vaccinated. at \$ \alpha = 0.01 \$, is there enough evidence to support the researchers claim? complete parts (a) through (d) below.

adult in the country who thinks that healthy children should be required to be vaccinated. state \$ h _ { 0 } \$ and \$ h _ { a } \$. select the correct choice below and fill in the answer boxes to complete your choice (round to two decimal places as needed.)

\$ \bigcirc \mathrm { a } \$ \$ h _ { 0 } : p \leq \$ \$ h _ { a } : p > \$ \$ \bigcirc \mathrm { b } \$ \$ h _ { 0 } : p < \$ \$ h _ { a } : p \geq \$ \$ \bigcirc \mathrm { c } \$ \$ h _ { 0 } : p = \$ \$ h _ { a } : p \
eq \$

\$ \bigcirc \mathrm { d } \$ \$ h _ { 0 } : p > \$ \$ h _ { a } : p \leq \$ \$ \bigcirc \mathrm { e } \$ \$ h _ { 0 } : p \
eq \$ \$ h _ { a } : p = \$ \$ \bigcirc \mathrm { f } \$ \$ h _ { 0 } : p \geq 0.80 \$ \$ h _ { a } : p < 0.80 \$

(b) find the critical value(s) and identify the rejection region(s)

identify the critical value(s) for this test.

\$ z _ { 0 } = - 2.33 \$

(round to two decimal places as needed. use a comma to separate answers as needed.)

identify the rejection region(s). select the correct choice below and fill in the answer box(es) to complete your choice (round to two decimal places as needed )

\$ \bigcirc \mathrm { a } \$. the rejection regions are \$ z < \$ and \$ z > \$

\$ \bigcirc \mathrm { b } \$. the rejection region is \$ z < \$

\$ \bigcirc \mathrm { c } \$. the rejection region is \$ z > \$

\$ \bigcirc \mathrm { d } \$. the rejection region is \$ < z < \$

Accepted Answer

# Explanation:
## Step1: Determine the type of hypothesis test
The researcher claims that less than 80% of adults think healthy children should be vaccinated. This is a left - tailed test.
## Step2: Recall the critical value for a left - tailed test
For a significance level $\alpha = 0.01$ in a left - tailed $z$ - test, we look up the value in the standard normal distribution table. The critical value $z_0$ is the value such that $P(Z<z_0)=\alpha$.
From the standard normal table, $z_0=- 2.33$
## Step3: Identify the rejection region
In a left - tailed test, the rejection region is all values of the test statistic $z$ that are less than the critical value.

# Answer:
B. The rejection region is $z < - 2.33$

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QUESTION IMAGE

Question

Explanation:

Step1: Determine the type of hypothesis test

Step2: Recall the critical value for a left - tailed test

Step3: Identify the rejection region

Answer: