In a sample of 45 mice, a biologist found that 40% were able to run a maze in 30 seconds or less. Find the 95% limit for the population proportion of mice who can run a maze in
30 seconds or less.
A) $25.7 \%

Question

In a sample of 45 mice, a biologist found that 40% were able to run a maze in 30 seconds or less. Find the 95% limit for the population proportion of mice who can run a maze in
30 seconds or less. 
A) $25.7 \% < p < 54.3 \%$
B) $28.0 \% < p < 52.0 \%$
C) $18.5 \% < p < 61.5 \%$
D) $32.8 \% < p < 47.2 \%$

Quizplus · Accepted Answer

To find the 95% confidence interval for the population proportion, we use the formula for the confidence interval of a proportion: $$p \pm Z \sqrt{\frac{p(1-p)}{n}}$$, where $p$ is the sample proportion, $Z$ is the Z-score for the desired confidence level (1.96 for 95%), and $n$ is the sample size. Given that 40% (or 0.4) of the 45 mice could run the maze in 30 seconds or less, we calculate the confidence interval as follows:$$0.4 \pm 1.96 \sqrt{\frac{0.4(0.6)}{45}}$$Calculating the margin of error:$$1.96 \sqrt{\frac{0.4(0.6)}{45}} \approx 0.147$$Thus, the 95% confidence interval is:$$0.4 - 0.147 < p < 0.4 + 0.147$$$$0.253 < p < 0.547$$Converting to percentages:$$25.3\% < p < 54.7\%$$The closest option to our calculated interval is:$25.7 \% < p < 54.3 \%$.

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In a Sample of 45 Mice, a Biologist Found That $25.7 \% < p < 54.3 \%$