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 years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 34 % developed cervical cancer, and based on a sample of 100 women in the placebo group, 44 % developed 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 = 0.05. Round 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 in the Gardisil group and p2 denotes the proportion of women who developed cervical cancer in the placebo group. Ho: P₁ Ha: P This test is left-tailed. What is the test statistic? -1.4497 P₂ P₂ Using your answer from the previous question, find the p-value. ▼ Part 2 of 4 Part 3 of 4

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**Cervical Cancer and HPV Vaccine Study**

Most cases of cervical cancer are linked to certain strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine, Gardasil, to target these HPV strains. In global clinical trials, young women were monitored for two to four years after receiving either the vaccine or a placebo to check for signs of HPV-related cervical cancer. The results from one sample of 100 women in the Gardasil group showed that 34% developed cervical cancer, compared to 44% in a sample of 100 women in the placebo group.

The objective is to test the claim that the proportion of women developing cervical cancer in the Gardasil group is less than in the placebo group, using a significance level of α = 0.05. Results should be rounded to three decimal places, with interim calculations to four decimal places.

**Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( p_1 = p_2 \) 
- Alternative Hypothesis (\( H_a \)): \( p_1 < p_2 \)

Where \( p_1 \) is the proportion of women who developed cervical cancer in the Gardasil group, and \( p_2 \) is the proportion in the placebo group. The test is left-tailed.

**Test Statistic:**
- Calculate the test statistic: -1.4497

Using the test statistic, find the p-value.
Transcribed Image Text:**Cervical Cancer and HPV Vaccine Study** Most cases of cervical cancer are linked to certain strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine, Gardasil, to target these HPV strains. In global clinical trials, young women were monitored for two to four years after receiving either the vaccine or a placebo to check for signs of HPV-related cervical cancer. The results from one sample of 100 women in the Gardasil group showed that 34% developed cervical cancer, compared to 44% in a sample of 100 women in the placebo group. The objective is to test the claim that the proportion of women developing cervical cancer in the Gardasil group is less than in the placebo group, using a significance level of α = 0.05. Results should be rounded to three decimal places, with interim calculations to four decimal places. **Hypotheses:** - Null Hypothesis (\( H_0 \)): \( p_1 = p_2 \) - Alternative Hypothesis (\( H_a \)): \( p_1 < p_2 \) Where \( p_1 \) is the proportion of women who developed cervical cancer in the Gardasil group, and \( p_2 \) is the proportion in the placebo group. The test is left-tailed. **Test Statistic:** - Calculate the test statistic: -1.4497 Using the test statistic, find the p-value.
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