Question

A realtor wishes to know what proportion of household occupants in the region own their home (as opposed to rent) within 0.08 at the 2% level of significance. How big a sample must be collected, if the true proportion is known to be at least 0.53?

Answer 1

To determine the required sample size, we use a formula that considers the desired level of significance, estimated proportion, and desired margin of error. In this case, the minimum sample size required is approximately 373.

Step-by-step explanation:

To calculate the required sample size, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

where:

• n is the required sample size
• Z is the Z-score corresponding to the desired level of significance (in this case, 2% level of significance is equivalent to a Z-score of approximately 2.33)
• p is the estimated proportion of household occupants owning their home (in this case, at least 0.53)
• E is the desired margin of error (0.08)

Substituting the values into the formula, we get:

n = (2.33^2 * 0.53 * (1 - 0.53)) / 0.08^2

n ≈ 372.43

Rounding up to the nearest whole number, the minimum sample size required is 373.