QuestionJuly 15, 2025

4. Estimating the population proportion, p, of all children from low income families who would draw the nickel too large. Give all answers correct to 3 decimal places. a) The best point estimate for the value of the population proportion p of all children from low income families who would draw the nickel too large is (hint: this number was an answer in an earlier question in this exam): square Next, find the 90% confidence interval for the population proportion of all children from low income families who would draw the nickel too large. b) Margin of error: square c) Confidence interval: square lt plt square d) Does the confidence interval support the claim that more than 40% of children from the low income group draw nickels too large? Confidence interval supports claim Confidence interval does not support claim

4. Estimating the population proportion, p, of all children from low income families who would draw the nickel too large. Give all answers correct to 3 decimal places. a) The best point estimate for the value of the population proportion p of all children from low income families who would draw the nickel too large is (hint: this number was an answer in an earlier question in this exam): square Next, find the 90% confidence interval for the population proportion of all children from low income families who would draw the nickel too large. b) Margin of error: square c) Confidence interval: square lt plt square d) Does the confidence interval support the claim that more than 40% of children from the low income group draw nickels too large? Confidence interval supports claim Confidence interval does not support claim
4. Estimating the population proportion, p, of all children from low income families who would draw the nickel too large. Give all answers correct to 3 decimal places. a) The best point estimate for the value of the population proportion p of all children from low income families who would draw the nickel too large is (hint: this number was an answer in an earlier question in this exam): square Next, find the 90% confidence interval for the population proportion of all children from low income families who would draw the nickel too large. b) Margin of error: square c) Confidence interval: square lt plt square d) Does the confidence interval support the claim that more than 40% of children from the low income group draw nickels too large? Confidence interval supports claim Confidence interval does not support claim

Solution
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Answer

a) Point estimate: \hat{p} ### b) Margin of error: E ### c) Confidence interval: \hat{p} - E < p < \hat{p} + E ### d) Confidence interval supports claim / does not support claim (based on evaluation in Step 4) Explanation 1. Identify the point estimate The best point estimate for the population proportion p is the sample proportion \hat{p}. This value should be provided from previous data or questions. 2. Calculate the margin of error Use the formula for margin of error at a 90\% confidence level: **E = Z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}**, where Z is the critical value for 90\% confidence (approximately 1.645), \hat{p} is the sample proportion, and n is the sample size. 3. Determine the confidence interval The confidence interval is calculated as \hat{p} - E < p < \hat{p} + E, using the margin of error E from Step 2. 4. Evaluate the claim Check if the entire confidence interval is above 0.40 to determine if it supports the claim that more than 40\% of children draw nickels too large.

Explanation

1. Identify the point estimate<br /> The best point estimate for the population proportion $p$ is the sample proportion $\hat{p}$. This value should be provided from previous data or questions.<br /><br />2. Calculate the margin of error<br /> Use the formula for margin of error at a $90\%$ confidence level: **$E = Z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$**, where $Z$ is the critical value for $90\%$ confidence (approximately 1.645), $\hat{p}$ is the sample proportion, and $n$ is the sample size.<br /><br />3. Determine the confidence interval<br /> The confidence interval is calculated as $\hat{p} - E < p < \hat{p} + E$, using the margin of error $E$ from Step 2.<br /><br />4. Evaluate the claim<br /> Check if the entire confidence interval is above $0.40$ to determine if it supports the claim that more than $40\%$ of children draw nickels too large.
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