Question Help A group of toxicologists investigated the impact of exposure to low oxygen on the mortality of rice weevils. In an experiment, 31,386 of 31,421 rice weevils were found dead after exposure to nitrogen gas for 4 days. In a second experiment, 23,516 of 23,676 rice weevils were found dead after exposure to nitrogen gas for 3.5 days. Conduct a test of hypothesis difference (at a = 0.10) in the mortality rates? compare the mortality rates of adult rice weevils exposed to nitrogen at the two exposure times. Is there a significant Give the null and alternative hypotheses. Let p, represent the proportion of rice weevils found dead in the first experiment and p, represent the proportion of rice weevils found dead in the second experiment. Choose the correct answer below. O A. Ho: (P1 - P2) #0 Ha: (P1 - P2) =0 OC. Ho: (P1 - P2) <0 Hạ: (P1 - P2) =0 OE. Ho: (P1 - P2) =0 H3: (P1 - P2) <0 B. Ho: (P1 -P2) =0 Ha: (P1 -P2) *0 OD. Ho: (P1 - P2) >0 Ha: (P1 -P2) =0 OF. Ho: (P1 -P2) =0 H3: (P1 -P2) >0 Find the test statistic. The test statistic is z=. (Round to two decimal places as needed.)

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### Study on the Mortality of Rice Weevils due to Nitrogen Gas Exposure

A group of toxicologists investigated the impact of low oxygen exposure on the mortality of rice weevils. 

#### Experimental Details:

- **First Experiment**: 
  - Sample Size: 31,421 rice weevils
  - Found Dead: 31,386 rice weevils
  - Exposure: Nitrogen gas for 4 days

- **Second Experiment**: 
  - Sample Size: 23,676 rice weevils
  - Found Dead: 23,516 rice weevils
  - Exposure: Nitrogen gas for 3.5 days

#### Objective:
Conduct a hypothesis test to compare the mortality rates of adult rice weevils exposed to nitrogen at the two different exposure times. Determine if there's a significant difference (at α = 0.10) in the mortality rates.

#### Formulate Hypotheses:
Let \( p_1 \) represent the proportion of rice weevils found dead in the first experiment and \( p_2 \) represent the proportion of rice weevils found dead in the second experiment.

The null and alternative hypotheses to test are:

**Option B:**
- Null Hypothesis (\( H_0 \)): \( (p_1 - p_2) = 0 \)
- Alternative Hypothesis (\( H_a \)): \( (p_1 - p_2) \neq 0 \)

#### Analysis:
Find the test statistic based on the provided proportions and sample sizes.

- The test statistic \( z \) is calculated as follows:
  \[
  z = \boxed{11.62}
  \]
  (Round to two decimal places as needed.)

This result helps in evaluating whether there's a significant difference in mortality rates of the rice weevils due to different exposure times to nitrogen gas.
Transcribed Image Text:### Study on the Mortality of Rice Weevils due to Nitrogen Gas Exposure A group of toxicologists investigated the impact of low oxygen exposure on the mortality of rice weevils. #### Experimental Details: - **First Experiment**: - Sample Size: 31,421 rice weevils - Found Dead: 31,386 rice weevils - Exposure: Nitrogen gas for 4 days - **Second Experiment**: - Sample Size: 23,676 rice weevils - Found Dead: 23,516 rice weevils - Exposure: Nitrogen gas for 3.5 days #### Objective: Conduct a hypothesis test to compare the mortality rates of adult rice weevils exposed to nitrogen at the two different exposure times. Determine if there's a significant difference (at α = 0.10) in the mortality rates. #### Formulate Hypotheses: Let \( p_1 \) represent the proportion of rice weevils found dead in the first experiment and \( p_2 \) represent the proportion of rice weevils found dead in the second experiment. The null and alternative hypotheses to test are: **Option B:** - Null Hypothesis (\( H_0 \)): \( (p_1 - p_2) = 0 \) - Alternative Hypothesis (\( H_a \)): \( (p_1 - p_2) \neq 0 \) #### Analysis: Find the test statistic based on the provided proportions and sample sizes. - The test statistic \( z \) is calculated as follows: \[ z = \boxed{11.62} \] (Round to two decimal places as needed.) This result helps in evaluating whether there's a significant difference in mortality rates of the rice weevils due to different exposure times to nitrogen gas.
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