Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four year for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 24% developed cervical cancer, and based on a sample of 100 women in the placebo group, 34 % develope cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.10. Roun your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer the Gardisil group and P2 denotes the proportion of women who developed cervical cancer in the place group. Ho: P. Ha: P. This test is left-tailed. What is the test statistic? P₂ P₂ Part

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### Study on Cervical Cancer and HPV Vaccine Efficacy

**Overview:**
Most cases of cervical cancer are linked to specific strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine called Gardasil targeting these HPV strains. A global clinical trial was conducted where young women received either the vaccine or a placebo, and were followed for two to four years for signs of HPV-induced cervical cancer.

**Study Results:**
- In a sample of 100 women who received the Gardasil vaccine, 24% developed cervical cancer.
- In a sample of 100 women who received a placebo, 34% developed cervical cancer.

**Objective:**
The study aims to test whether the proportion of women who developed cervical cancer in the Gardasil group is less than that in the placebo group, with the significance level set at \( \alpha = 0.10 \).

**Hypothesis Testing:**

- **Null Hypothesis (\( H_0 \)):**
  - \( p_1 = p_2 \)
  - \( p_1 \) denotes the proportion in the Gardasil group.
  - \( p_2 \) denotes the proportion in the placebo group.

- **Alternative Hypothesis (\( H_a \)):**
  - \( p_1 < p_2 \)

**Test Type:**
- This is a left-tailed test.

**Statistical Analysis:**
The test statistic is not provided in the transcription but would be calculated based on the sample data to determine if the observed difference in proportions is statistically significant.

Please enter the test statistic in the designated section when calculated.
Transcribed Image Text:### Study on Cervical Cancer and HPV Vaccine Efficacy **Overview:** Most cases of cervical cancer are linked to specific strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine called Gardasil targeting these HPV strains. A global clinical trial was conducted where young women received either the vaccine or a placebo, and were followed for two to four years for signs of HPV-induced cervical cancer. **Study Results:** - In a sample of 100 women who received the Gardasil vaccine, 24% developed cervical cancer. - In a sample of 100 women who received a placebo, 34% developed cervical cancer. **Objective:** The study aims to test whether the proportion of women who developed cervical cancer in the Gardasil group is less than that in the placebo group, with the significance level set at \( \alpha = 0.10 \). **Hypothesis Testing:** - **Null Hypothesis (\( H_0 \)):** - \( p_1 = p_2 \) - \( p_1 \) denotes the proportion in the Gardasil group. - \( p_2 \) denotes the proportion in the placebo group. - **Alternative Hypothesis (\( H_a \)):** - \( p_1 < p_2 \) **Test Type:** - This is a left-tailed test. **Statistical Analysis:** The test statistic is not provided in the transcription but would be calculated based on the sample data to determine if the observed difference in proportions is statistically significant. Please enter the test statistic in the designated section when calculated.
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