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.

Answer 1

Based on the question, here are the given information:

n = 40 mice as sample

x ≤ 30 seconds

proportion (p) = 42% or 0.42 in decimal form

Find: 90% limit or confidence interval

Solution:

The formula in getting the confidence interval in proportion is:

`CI=p\pm Z(\sqrt[]{(p(1-p))/(n)}`

Recall that for 90% confidence interval, the z-value is 1.645. Since we already have the values of "p" and "n" given in the problem, let's plug these values into the formula above.

`CI=0.42\pm1.645\sqrt[]{(0.42(1-0.42))/(40)}`

Then, solve.

`\begin{gathered} CI=0.42\pm1.645\sqrt[]{(0.42*0.58)/(40)} \\ CI=0.42\pm1.645\sqrt[]{(0.2436)/(40)} \\ CI=0.42\pm1.645(0.078038) \\ CI=0.42\pm0.12837 \end{gathered}`

Separate the plus and minus signs.

`\begin{gathered} CI=0.42+0.12837=0.54837\Rightarrow54.8percent \\ CI=0.42-0.12837=0.29163\Rightarrow29.2percent \end{gathered}`

Hence, the 90% limit of the proportion is between 29.2% to 54.8%. Based on the options, the answer is 29.1% < p < 54.9% (third option).

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