A researcher wants to assess if there is a difference in the average life spans between men and women in Japan. Let μ₁ = average life span of Japanese women and μ₂ = average life span of Japanese men. A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years. A random sample of 10 men showed an average lifespan of 77 years, with a sample standard deviation of 6.4 years. Assume that life spans are normally distributed and that the population variances are equal. What is the p-value? Between .05 and .10 O Greater than .10 Between .01 and .025 O Between .02 and .05 O Between .025 and .05 O Less than .01

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**Assessment of Average Lifespans Between Genders in Japan**

A researcher aims to determine if there is a significant difference in the average lifespans of men and women in Japan. 

- Let μ₁ represent the average lifespan of Japanese women.
- Let μ₂ represent the average lifespan of Japanese men.

### Sample Information

- **Women:**
  - Sample Size (n₁): 10
  - Average Lifespan: 83 years
  - Sample Standard Deviation: 7 years

- **Men:**
  - Sample Size (n₂): 10
  - Average Lifespan: 77 years
  - Sample Standard Deviation: 6.4 years

### Assumptions

- Lifespans are normally distributed.
- Population variances are equal.

### Hypothesis Testing

The goal is to determine the p-value for the observed data.

### Question

*What is the p-value?*

### Possible Answers

- Between .05 and .10 
- Greater than .10
- Between .01 and .025
- Between .02 and .05
- Between .025 and .05
- Less than .01

**Selected Answer: Between .05 and .10**

This information helps in understanding if the observed difference in average lifespans between men and women in Japan is statistically significant.
Transcribed Image Text:**Assessment of Average Lifespans Between Genders in Japan** A researcher aims to determine if there is a significant difference in the average lifespans of men and women in Japan. - Let μ₁ represent the average lifespan of Japanese women. - Let μ₂ represent the average lifespan of Japanese men. ### Sample Information - **Women:** - Sample Size (n₁): 10 - Average Lifespan: 83 years - Sample Standard Deviation: 7 years - **Men:** - Sample Size (n₂): 10 - Average Lifespan: 77 years - Sample Standard Deviation: 6.4 years ### Assumptions - Lifespans are normally distributed. - Population variances are equal. ### Hypothesis Testing The goal is to determine the p-value for the observed data. ### Question *What is the p-value?* ### Possible Answers - Between .05 and .10 - Greater than .10 - Between .01 and .025 - Between .02 and .05 - Between .025 and .05 - Less than .01 **Selected Answer: Between .05 and .10** This information helps in understanding if the observed difference in average lifespans between men and women in Japan is statistically significant.
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