The 95% confidence interval for the proportion of all high school students who had smoked cigarettes in the past year, was found to be (0.496, 0.594). Suppose that an error was made in recording the survey data and that instead of 218 students, the actual number of students who indicated that they had smoked cigarettes in the past year was 318 students. How would the 95% confidence interval change?
A.
The width of the confidence interval would be wider
B.
The width of the confidence interval would be narrower
C.
The width of the confidence interval would be the same
A. The width of the confidence interval would be wider
A. The width of the confidence interval would be wider.
To understand how the 95% confidence interval would change, we need to consider the formula for calculating the confidence interval for proportions. The formula is (p̂ ± z √(p̂(1-p̂)/n)), where p̂ is the sample proportion, z is the z-score corresponding to the desired level of confidence (95% in this case), and n is the sample size.
In the given scenario, the original sample proportion p̂ was calculated based on a sample size of 218 students, resulting in a 95% confidence interval from 0.496 to 0.594. Now, the number of students indicating smoking is recorded as 318. However, we don't have the updated sample size.
To determine how the 95% confidence interval would change, we need to know the new sample size. Without that information, we cannot directly calculate the revised confidence interval. It's important to note that if the sample size increases, the interval will generally become narrower; whereas, if the sample size decreases, the interval will expand.
Therefore, based on the given information, we cannot determine whether the width of the confidence interval would be wider, narrower, or the same without knowing the updated sample size.