The heights of young American women, in inches, are normally distributed with mean mu and standard deviation 2.4 (sigma). I select a simple random sample of four young American women and measure their heights. The four heights, in inches, are
63 69 62 66
If I want the margin of error for a 99% confidence interval to be +/- 1 inch, I should select a simple random sample of size
(Points: 2)
A. 2.
B. 7
C. 16
D. 39.
8 years ago
1 year ago
To find the sample size required for a specific margin of error, we can use the formula:
n = (z * sigma / E)^2
where:
n = sample size
z = z-score corresponding to the desired confidence level (99% confidence level corresponds to z = 2.576)
sigma = standard deviation of the population
E = margin of error
Given that sigma = 2.4 and E = 1, we can substitute these values into the formula:
n = (2.576 * 2.4 / 1)^2
n ≈ 37.29
Since the sample size must be a whole number, we round up to the nearest whole number.
Therefore, the correct answer is D. 39.
1 year ago
To calculate the margin of error, we can use the formula:
Margin of Error = (Z-value) * (Standard Deviation / Square Root of Sample Size)
We want the margin of error to be +/- 1 inch. Since we want a 99% confidence interval, the Z-value corresponding to a 99% confidence level is approximately 2.576 (you can look up this value in a standard normal distribution table).
Let's solve for the sample size (N) in the formula:
1 = (2.576) * (2.4 / sqrt(N))
Dividing both sides of the equation by 2.576 * 2.4, we get:
1 / (2.576 * 2.4) = sqrt(N)
Taking the square root of both sides:
sqrt(1 / (2.576 * 2.4)) = sqrt(N)
Simplifying the expression:
sqrt(1 / 6.1824) = sqrt(N)
1 / sqrt(6.1824) = sqrt(N)
0.2597 = sqrt(N)
Squaring both sides:
0.0675 = N
Therefore, N is approximately 0.0675. Since the sample size must be a whole number, we should round up to the nearest whole number. Therefore, the sample size should be:
N = 1
This means that we would need to select a sample size of 1 young American woman to achieve a margin of error of +/- 1 inch for a 99% confidence interval. However, since we were given a sample of 4 heights, it seems that the margin of error requirement cannot be met with the given sample size.
Therefore, the correct answer is none of the options provided.