Question

In an experiment using 30 mice, the sample proportion of the mice that gained weight after a drug injection is 0.65. What is the 99.7% confidence interval for the actual proportion in the population? Which measure is the same as the standard error of the mean?

a) 0.65 ± 0.02; Margin of error
b) 0.65 ± 0.05; Standard deviation
c) 0.65 ± 0.10; Confidence interval
d) 0.65 ± 0.15; Standard error

Answer 1

The 99.7% confidence interval for the actual proportion in the population is 0.65 ± 0.1489. The standard error of the mean is 0.65 ± 0.15.

Step-by-step explanation:

The 99.7% confidence interval for the actual proportion in the population can be calculated using the formula:

CI = p ± z * sqrt((p * (1-p))/n)

Where CI is the confidence interval, p is the sample proportion, z is the z-score corresponding to the desired confidence level, and n is the sample size.

For a 99.7% confidence level, the z-score is approximately 2.967. Plugging in the values, we get:

CI = 0.65 ± 2.967 * sqrt((0.65 * (1-0.65))/30)

Simplifying the equation gives us:

CI = 0.65 ± 0.1489

Therefore, the 99.7% confidence interval for the actual proportion in the population is 0.65 ± 0.1489.

The measure that is the same as the standard error of the mean is d) 0.65 ± 0.15; Standard error.