Question

in 1976, the standard deviation of female height in the us was found to be 2.7 inches. how large a sample is required in order for 95% confidence interval of width to be 0.202 inches?

Answer 1

To calculate the required sample size for a 95% confidence interval width of 0.202 inches, use the formula n = (Z * σ) / E, where n is the required sample size, Z is the z-value for the desired confidence level, σ is the standard deviation, and E is the margin of error.

Step-by-step explanation:

To calculate the sample size required for a 95% confidence interval width of 0.202 inches, we can use the formula:

n = (Z * σ) / E

Where:

• n is the required sample size
• Z is the z-value corresponding to the desired confidence level (e.g., 1.96 for a 95% confidence level)
• σ is the standard deviation
• E is the desired margin of error (half the width of the confidence interval)

Plugging in the values from the question:

n = (1.96 * 2.7) / 0.202

n ≈ 26.24

So, a sample size of at least 27 would be required to achieve a 95% confidence interval width of 0.202 inches.