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. children should be required to be vaccinated is not % b. more than % of adults in the country think that healthy children should be required to be vaccinated c. less than 80% of adults in the country think that healthy children should be required to be vaccinated d. % of adults in the country think that healthy children should be required to be vaccinated let \\( p \\) be the population proportion of successes, where a success is an 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.) a. \\( h _ { 0 } : p \leq \\) \\( h _ { a } : p > \\) b. \\( h _ { 0 } : p < \\) \\( h _ { a } : p \geq \\) c. \\( h _ { 0 } : p = \\) \\( h _ { a } : p \
eq \\) d. \\( h _ { 0 } : p > \\) \\( h _ { a } : p \leq \\) e. \\( h _ { 0 } : p \
eq \\) \\( h _ { a } : p = \\) 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 } = \\) (round to two decimal places as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Determine the type of test

Since the claim is "less than 80%", this is a left - tailed test.

Step2: Find the critical value

For a left - tailed test with \(\alpha = 0.01\), we look up the \(z\) - value in the standard normal distribution table. The critical value \(z_0\) is the \(z\) - value such that \(P(Z<z_0)=\alpha = 0.01\).
Using the standard normal table or a calculator, \(z_0=- 2.33\)

Answer:

\(z_0=-2.33\)