**Title: Analyzing Medication Side Effects Using Hypothesis Testing****Introduction:**Researchers conducted a study involving 894 patients selected randomly from a group regularly using a specific prescription drug. During the clinical trial, 24 of these patients reported experiencing flu-like symptoms. The objective is to determine if there is significant evidence that more than 2.4% of the drug's users experience these symptoms as a side effect, using a significance level of α = 0.01.**Data Analysis:**1. **Significance Condition:** - Given: - Probability of side effect, \( p_0 = 0.024 \) - Sample size, \( n = 894 \) - Number experiencing side effects, \( x = 24 \) - Calculation for \( np_0(1 - p_0): \) \[ np_0(1 - p_0) = 20.9 > 10 \] - Conclusion: Sample size conditions are satisfied. - Sample size less than 5% of the population: This condition supports the appropriateness of the sample size.2. **Hypotheses:** - Null Hypothesis (\( H_0 \)): \( p = 0.024 \) - Alternative Hypothesis (\( H_1 \)): \( p > 0.024 \)3. **Test Statistic:** - Formula for \( z_0 \) (not fully provided in the image): \[ z_0 = \, \text{(Calculation Required. Round to two decimal places as needed.)} \]**Conclusion:**The study's design follows all necessary conditions for hypothesis testing. The goal is to calculate the test statistic (\( z_0 \)) and compare it with critical values to determine if the null hypothesis can be rejected, indicating a statistically significant greater incidence of flu-like symptoms above the established 2.4% threshold.

om among those who take a certain widely-used prescription drug daily. In a clinical trial, 24 out of the 894 patients complained of flulike symptoms. Suppose that it is known that amplain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.4% of this drug's users experience flulike symptoms as a side effect at the a=0.01 level of sample size is less than 5% of the population size, and the patients in the sample es? > 0.024 needed) were selected at random, all of the requirements for testing the hypothesis are

om among those who take a certain widely-used prescription drug daily. In a clinical trial, 24 out of the 894 patients complained of flulike symptoms. Suppose that it is known that amplain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.4% of this drug's users experience flulike symptoms as a side effect at the a=0.01 level of sample size is less than 5% of the population size, and the patients in the sample es? > 0.024 needed) were selected at random, all of the requirements for testing the hypothesis are

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

**Title: Analyzing Medication Side Effects Using Hypothesis Testing**

**Introduction:**

Researchers conducted a study involving 894 patients selected randomly from a group regularly using a specific prescription drug. During the clinical trial, 24 of these patients reported experiencing flu-like symptoms. The objective is to determine if there is significant evidence that more than 2.4% of the drug's users experience these symptoms as a side effect, using a significance level of α = 0.01.

**Data Analysis:**

1. **Significance Condition:**
- Given:
- Probability of side effect, \( p_0 = 0.024 \)
- Sample size, \( n = 894 \)
- Number experiencing side effects, \( x = 24 \)
- Calculation for \( np_0(1 - p_0): \)
\[
np_0(1 - p_0) = 20.9 > 10
\]
- Conclusion: Sample size conditions are satisfied.
- Sample size less than 5% of the population: This condition supports the appropriateness of the sample size.

2. **Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( p = 0.024 \)
- Alternative Hypothesis (\( H_1 \)): \( p > 0.024 \)

3. **Test Statistic:**
- Formula for \( z_0 \) (not fully provided in the image):
\[
z_0 = \, \text{(Calculation Required. Round to two decimal places as needed.)}
\]

**Conclusion:**

The study's design follows all necessary conditions for hypothesis testing. The goal is to calculate the test statistic (\( z_0 \)) and compare it with critical values to determine if the null hypothesis can be rejected, indicating a statistically significant greater incidence of flu-like symptoms above the established 2.4% threshold.

Expert Solution

Step 1: By using the given data:

Answer

Given

The population proportion [p0] = 0.024

The favorable cases [x] = 24

The sample size [n] =894

The sample proportion =P̂ = x/n = 0.0268

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Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Researchers selected 894 patients at random among those who take a certain widely-used prescription drug daily. In a clinical trial, 24 out of the 894 patients complained of flulike symptoms. Suppose that it is known that 2.4% of
patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.4% of this drug's users experience flulike symptoms as a side effect at the x = 0.01 level of significance?
Because npo (1-Po) = 20.9 > 10, the sample size is
(Round to one decimal place as needed.)
What are the null and alternative hypotheses?
0.024 versus H₁: p > 0.024
Ho: P
(Type integers or decimals. Do not round.)
Find the test statistic, Zo.
Zo=
= 0.55 (Round to two decimal places as needed.)
Find the P-value.
P-value = 0.291 (Round to three decimal places as needed.)
Interpret the results.
Since the P-value is
complained of flulike symptoms.
(Type integers or decimals. Do not round.)
than α,
less than 5% of the population size, and the patients in the sample were selected at random, all of the requirements for testing the hypothesis are satisfied.
the null hypothesis. There
sufficient evidence at the α =
level of significance to conclude that
% of the users who take the prescription drug daily

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Follow-up Question

**Find the P-value**

**P-value =** [ ] *(Round to three decimal places as needed.)*

This section prompts students to calculate and enter the P-value based on a given statistical context. The instruction emphasizes rounding the calculated P-value to three decimal places for precision in reporting results.

**Note:** There are no graphs or diagrams accompanying this text.

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