A genetic experiment with peas resulted in one sample of offspring that consisted of 403 green peas and 151 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow? a. Construct a 95% confidence interval. Express the percentages in decimal form.
A genetic experiment with peas resulted in one sample of offspring that consisted of 403 green peas and 151 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow? a. Construct a 95% confidence interval. Express the percentages in decimal form.
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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### Genetic Experiment with Peas
A genetic experiment with peas resulted in one sample of offspring that consisted of 403 green peas and 151 yellow peas.
#### Questions:
**a. Construct a 95% confidence interval to estimate the percentage of yellow peas.**
- Express the percentages in decimal form.
- \( \_\_\_\_\_ < p < \_\_\_\_\_ \) (Round to three decimal places as needed).
**b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?**
- Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%
- No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
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#### Explanation of Concepts:
To address these questions, you need to calculate the 95% confidence interval for the proportion of yellow peas.
1. **Calculate the sample proportion (p̂)**:
\( p̂ = \frac{\text{number of yellow peas}}{\text{total number of peas}} \)
In this case:
\( p̂ = \frac{151}{403 + 151} = \frac{151}{554} \)
2. **Calculate the standard error (SE)**:
\( \text{SE} = \sqrt{\frac{p̂ (1 - p̂)}{n}} \)
Here, \( n \) is the total number of peas (554).
3. **Determine the Z-value for a 95% confidence level**:
The Z-value is typically 1.96 for a 95% confidence interval.
4. **Construct the confidence interval**:
\( CI = p̂ \pm (Z \times \text{SE}) \)
- **Interpret the Confidence Interval**:
Once you have calculated the confidence interval, compare it with 0.25 to determine if it includes this value, to address part (b) of the question.
Note: The detailed calculations will provide you with the range which can be used to interpret whether 0.25 lies within this interval or not.
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