Question

An agency surveyed people worldwide, asking them, "Do you live in a household with more than one car?" Of the 1399 respondents surveyed in India, 307 said they live in a household with more than one car. In Canada, of the 809 respondents, 584 said they lived in a household with more than one car. Find the lower limit for a 99% confidence interval for the difference in the proportions of households with more than one car between India and Canada ( Pᵢ – P), assuming 20.005 = 2. 58.

Answer 1

To find the lower limit for a 99% confidence interval for the difference in proportions of households with more than one car between India and Canada, we can use a formula that takes into account the proportions, sample sizes, and the desired confidence level.

Step-by-step explanation:

To find the lower limit for a 99% confidence interval for the difference in proportions of households with more than one car between India and Canada, we can use the formula:

Lower Limit = (Pᵢ - P) - (z * √((Pᵢ * (1 - Pᵢ)) / nᵢ + P * (1 - P) / n))

where:

• Pᵢ is the proportion of households with more than one car in India
• P is the proportion of households with more than one car in Canada
• z is the z-score corresponding to the desired confidence level (in this case, 2.58)
• nᵢ is the number of respondents surveyed in India
• n is the number of respondents surveyed in Canada

Using the given information, we have:

• Pᵢ = 307/1399
• P = 584/809
• z = 2.58
• nᵢ = 1399
• n = 809

Plugging these values into the formula, we can calculate the lower limit for the confidence interval.