A study based on a sample of size 25 reported a mean of 94 with a margin of error of 15 for 95% confidence
(a) Give the 95% confidence interval.
(__________,________)
(b) If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than 15?
Explain your answer.
pick one
The new margin of error would be equal to 15. The margin of error will not change when the confidence level is increased.
The new margin of error would be less than 15. A smaller margin of error is needed to be more confident that the interval includes the true mean.
The new margin of error would be greater than 15. A wider margin of error is needed to be more confident that the interval includes the true mean.
It is impossible to determine if the margin of error will change using the information given.
The confidence level should never be changed for the same study.
(a) To calculate the 95% confidence interval, we use the formula:
95% confidence interval = (mean - margin of error, mean + margin of error)
In this case, the mean is 94, and the margin of error is 15. Plugging these values into the formula, we get:
95% confidence interval = (94 - 15, 94 + 15)
Therefore, the 95% confidence interval is (79, 109).
(b) The new margin of error for a 99% confidence level would be greater than 15. As the confidence level increases, we need to be more confident that the interval includes the true mean. To achieve a higher level of confidence, we need to widen the margin of error. Thus, the margin of error would increase if we wanted 99% confidence for the same study.