In a sample of 40 mice, a biologist found that 42% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run a maze in 30 seconds or less.
A) 35.6%

Question

In a sample of 40 mice, a biologist found that 42% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run a maze in 30 seconds or less.
A) 35.6% < p < 48.4%
B) 32.0% < p < 52.0%
C) 29.1% < p < 54.9%
D) 22.7% < p < 61.3%

Quizplus · Accepted Answer

To find the 90% limit for the population proportion, we can use the formula:
p ± z*sqrt(p*(1-p)/n) 
where p is the sample proportion, z is the z-score corresponding to the desired level of confidence (90%), and n is the sample size.

First, we need to find the z-score for the 90% confidence level. This can be found using a standard normal distribution table or a calculator, and it is approximately 1.645.

Next, we plug in the values we know from the problem:
p = 0.42 (sample proportion)
z = 1.645 (z-score for 90% confidence)
n = 40 (sample size)

p ± z*sqrt(p*(1-p)/n) 
= 0.42 ± 1.645*sqrt(0.42*0.58/40) 
= 0.42 ± 0.132 
= 0.288 to 0.552

Therefore, the 90% limit for the population proportion of mice who can run a maze in 30 seconds or less is 29.1% to 54.9%. The closest answer choice is C.

In a Sample of 40 Mice, a Biologist Found That