Question

Two studies were completed in California. One study in northern California involved 1,000 patients; 74% of them experienced flulike symptoms during the month of December. The other study, in southern California, involved 500 patients; 34% of them experienced flulike symptoms during the same month. Which study has the smallest margin of error for a 98% confidence interval?

The northern California study with a margin of error of 3.2%.
The southern California study with a margin of error of 3.2%.
The northern California study with a margin of error of 4.9%.
The southern California study with a margin of error of 4.9%.

Answer 1

The correct answer is: The northern California study with a margin of error of 3.2% has the smallest margin of error for a 98% confidence interval.

Step-by-step explanation:

In order to determine which study has the smallest margin of error for a 98% confidence interval, we need to find the margin of error for each study and compare them. The margin of error is calculated using the formula: margin of error = z * sqrt((p * (1-p))/n), where z is the z-score for the desired confidence level, p is the proportion of the population with the characteristic of interest, and n is the sample size.

For the northern California study:

Sample size (n) = 1000; Proportion (p) = 0.74

For the southern California study:

Sample size (n) = 500; Proportion (p) = 0.34

Using a z-score of 2.33 for a 98% confidence level, the margin of error for the northern California study is 3.2% and the margin of error for the southern California study is 4.9%.

Therefore, the correct answer is: The northern California study with a margin of error of 3.2% has the smallest margin of error for a 98% confidence interval.

Answer 2

The right answer for the question that is being asked and shown above is that: "The southern California study with a margin of error of 4.9%." the study has the smallest margin of error for a 98% confidence interval is that The southern California study with a margin of error of 4.9%.