Question

Using the appropriate formulas, in the space provided, determine the sample sizes of the following cases: Case i). Variability of 30%, confidence level of 95%, and allowabje error of ±5%.

Answer 1

To determine the sample size for a confidence interval, you can use the formula: n = (Z * σ) / E, where n is the sample size, Z is the z-score corresponding to the desired confidence level, σ is the variability, and E is the allowable error. In this case, the sample size is 12.

Step-by-step explanation:

To determine the sample size for a confidence interval, we can use the formula:

n = (Z * σ) / E

Where:

n is the sample size

Z is the z-score corresponding to the desired confidence level

σ is the variability

E is the allowable error

In this case, the variability is 30%, the confidence level is 95%, and the allowable error is ±5%. The z-score for a 95% confidence level is 1.96. Plugging these values into the formula, we get:

n = (1.96 * 0.3) / 0.05 = 11.76

Rounding up to the nearest whole number, the sample size is 12.