4. Amedical researcher says that less than 8/% of adults in a certain country think that healthy children should be required to be vacčináted. In a random sample of 400 adults in that country, 85% think that healthy children should be required to be vaccinated. At a0.01, is there enough evidence to support the researe claim? Complete parts (a) through (e) below. (a) Identify the claim and state Ho and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. Less than % of adults in the country think that healthy children should be required to be vaccinated. O B. More than % of adults in the country think that healthy children should be required to be vaccinated. Oc. % of adults in the country think that healthy children should be required to be vaccinated. OD. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not 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 Ho and H Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) OA. Hạ p= OB. Họ pa OC. Ha: ps H, p OD. He p> Haip< H, p> OE. H: p< OF. H p H, p H, ps H, p2 (b) Find the critical value(s) and identify the rejection region(s). Identify the critical value(s) for this test. (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.) O A. The rejection region is z> OB. The rejection region is Oc. The rejection region is z < OD. The rejection regions are z< and z> (c) Find the standardized test statistic z. (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim (1). the null hypothesis. There (2) enough evidence to (3) the researcher's claim (1) O Fail to reject (2) O is not (3) O reject O Reject O sunnort

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**Problem 4: Statistical Analysis of Vaccination Opinions**

A medical researcher claims that less than 87% of adults in a certain country believe healthy children should be required to be vaccinated. In a random sample of 400 adults in that country, 85% think healthy children should be required to be vaccinated. At a significance level of α = 0.01, determine if there is sufficient evidence to support the researcher's claim.

**Steps to Analyze the Claim:**

(a) **Identify the Claim and Formulate Hypotheses:**
- Identify the claim in the scenario.
- Options for hypothesis formulation (select one and fill in the blanks):
  - Less than ___% of adults in the country think that healthy children should be required to be vaccinated.
  - More than ___% of adults in the country think that healthy children should be required to be vaccinated.
  - ___% of adults in the country think that healthy children should be required to be vaccinated.
  - The percentage of adults in the country who think healthy children should be required to be vaccinated is not ___%.
  
- Let \( p \) represent the population proportion of adults believing in mandatory vaccination for healthy children.
- Select the appropriate null (\( H_0 \)) and alternative (\( H_1 \)) hypotheses:
  - A. \( H_0: p = \) ___, \( H_1: p < \) ___
  - B. \( H_0: p \geq \) ___, \( H_1: p < \) ___
  - C. \( H_0: p \leq \) ___, \( H_1: p > \) ___
  - D. \( H_0: p = \) ___, \( H_1: p > \) ___
  - E. \( H_0: p \leq \) ___, \( H_1: p > \) ___
  - F. \( H_0: p \neq \) ___, \( H_1: p = \) ___

(b) **Find the Critical Value(s) and Identify the Rejection Region(s):**
- Determine the critical value \( z_0 = \) ___ for this test.
  - (Round to two decimal places.)

- Identify the rejection region(s):
  - A. The rejection region is \( z > \) ___
  - B. The rejection region is
Transcribed Image Text:**Problem 4: Statistical Analysis of Vaccination Opinions** A medical researcher claims that less than 87% of adults in a certain country believe healthy children should be required to be vaccinated. In a random sample of 400 adults in that country, 85% think healthy children should be required to be vaccinated. At a significance level of α = 0.01, determine if there is sufficient evidence to support the researcher's claim. **Steps to Analyze the Claim:** (a) **Identify the Claim and Formulate Hypotheses:** - Identify the claim in the scenario. - Options for hypothesis formulation (select one and fill in the blanks): - Less than ___% of adults in the country think that healthy children should be required to be vaccinated. - More than ___% of adults in the country think that healthy children should be required to be vaccinated. - ___% of adults in the country think that healthy children should be required to be vaccinated. - The percentage of adults in the country who think healthy children should be required to be vaccinated is not ___%. - Let \( p \) represent the population proportion of adults believing in mandatory vaccination for healthy children. - Select the appropriate null (\( H_0 \)) and alternative (\( H_1 \)) hypotheses: - A. \( H_0: p = \) ___, \( H_1: p < \) ___ - B. \( H_0: p \geq \) ___, \( H_1: p < \) ___ - C. \( H_0: p \leq \) ___, \( H_1: p > \) ___ - D. \( H_0: p = \) ___, \( H_1: p > \) ___ - E. \( H_0: p \leq \) ___, \( H_1: p > \) ___ - F. \( H_0: p \neq \) ___, \( H_1: p = \) ___ (b) **Find the Critical Value(s) and Identify the Rejection Region(s):** - Determine the critical value \( z_0 = \) ___ for this test. - (Round to two decimal places.) - Identify the rejection region(s): - A. The rejection region is \( z > \) ___ - B. The rejection region is
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