a genetic experiment with peas resulted in one sample of offspring that consisted of 448 green peas and 169 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.
$\square

Question

a genetic experiment with peas resulted in one sample of offspring that consisted of 448 green peas and 169 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.
$\square < p < \square$ (round to three decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "One-Sample Proportion Confidence Interval", "Margin of Error for Proportions" ], "current_concepts": [ "One-Sample Proportion Confidence Interval", "Margin of Error for Proportions", "Z-critical Value" ] } ## Calculate sample statistics $$ \begin{aligned} x &= 169 \quad (\text{yellow peas}) \ n &= 448 + 169 = 617 \quad (\text{total offspring}) \ \hat{p} &= \frac{169}{617} \approx 0.273906 \end{aligned} $$ ## Compute standard error and margin of error $$ \begin{aligned} z_{\alpha/2} &= 1.96 \quad (\text{for } 95\% \text{ confidence}) \ SE &= \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = \sqrt{\frac{0.273906 \times 0.726094}{617}} \approx 0.017946 \ E &= z_{\alpha/2} \times SE = 1.96 \times 0.017946 \approx 0.035174 \end{aligned} $$ ## Determine confidence interval limits $$ \begin{aligned} \text{Lower Limit} &= \hat{p} - E = 0.273906 - 0.035174 \approx 0.238732 \approx 0.239 \ \text{Upper Limit} &= \hat{p} + E = 0.273906 + 0.035174 \approx 0.309080 \approx 0.309 \end{aligned} $$ a. Construct a 95% confidence interval. Express the percentages in decimal form. 0.239 $< p <$ 0.309 (Round to three decimal places as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "One-Sample Proportion Confidence Interval" ] }

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Question

Explanation:

Calculate sample statistics

Compute standard error and margin of error

Determine confidence interval limits

Answer: