Question

The standard iq test has a mean of 105 and a standard deviation of 17. we want to be 90% certain that we are within 2 iq points of the true mean. determine the required sample size.

Answer 1

To determine the required sample size, use the formula n = (Z * σ / E)², where n is the required sample size, Z is the Z-score representing the desired level of confidence, σ is the standard deviation of the population, and E is the desired margin of error. Substituting the given values, the required sample size is approximately 196.

Step-by-step explanation:

To determine the required sample size, we need to use the formula for sample size calculation. The formula is:

n = (Z * σ / E)²

Where:

• n is the required sample size
• Z is the Z-score representing the desired level of confidence (in this case, it is the Z-score for a 90% confidence level, which is approximately 1.645)
• σ is the standard deviation of the population (in this case, it is 17)
• E is the desired margin of error (in this case, it is 2)

Substituting the values into the formula, we get:

n = (1.645 * 17 / 2)²

n = (27.965 / 2)²

n = 13.9825²

n ≈ 195.64

Rounding up to the nearest whole number, the required sample size is 196.