Question

A real estate conglomerate in California wants to investigate home ownership in Texas. How many people should be surveyed to determine the proportion of Texans who own their own homes, given a recent poll showing 68.3% homeownership? Construct a 99% confidence interval with a 5% margin of error.

Answer 1

To determine the proportion of Texans who own their own homes, you need to calculate the sample size needed to construct a 99% confidence interval with a 5% margin of error.

Step-by-step explanation:

To determine the proportion of Texans who own their own homes, you need to calculate the sample size needed to construct a 99% confidence interval with a 5% margin of error.

The formula for calculating the sample size is:

n = (Z^2 * p * q) / E^2

Where:

• n is the required sample size
• Z is the Z-score corresponding to the desired confidence level (99% corresponds to a Z-score of approximately 2.58)
• p is the estimated proportion of homeownership (68.3%)
• q is 1 - p (31.7%)
• E is the desired margin of error (5% corresponds to 0.05)

Plugging in the values:

n = (2.58^2 * 0.683 * 0.317) / 0.05^2 = 682

Therefore, you should survey at least 682 people to determine the proportion of Texans who own their own homes.