Question

In finding a confidence interval for a random sample of 35 students' GPAs, one interval was (2.45,3.25) and the other was (2.55,3.15).

a. One of them is a 95% interval and one is a 90% interval. Which is which, and how do you know?
b. If we used a larger sample size (n=140 instead of n=35, would the 95% interval be wider or narrower than the one reported here?
a. Choose the correct answer below. A. The interval (2.55,3.15) is the 95% interval and (2.45,3.25) is the 90% interval- −90% of the data points fall between 2.45 and 3.25 .
B. The interval (2.55,3.15) is the 95% interval and (2.45,3.25) is the 90% interval-a higher level of confidence results in a narrower confidence interval.
C. The interval (2.45,3.25) is the 95% interval and (2.55,3.15) is the 90% interval-a higher level of confidence results in a wider confidence interval.
D. The interval (2.45,3.25) is the 95% interval and (2.55,3.15) is the 90% interval- −95% of the data points fall between 2.45 and 3.25 .
b. The 95% interval with n=140 will be than the interval with n=35 because a larger sample size provides a standard error, and this means a margin of error at the same level of confidence. smaller larger In finding a confidence interval for a random sample of 35 students' GPAs, one interval was (2.45,3.25) and the other was (2.55, 3.15).
a. One of them is a 95% interval and one is a 90% interval. Which is which, and how do you know?
b. If we used a larger sample size (n=140 instead of n=35, would the 95% interval be wider or narrower than the one reported here?
a. Choose the correct answer below. A. The interval (2.55,3.15) is the 95% interval and (2.45,3.25) is the 90% interval −90% of the data points fall between 2.45 and 3.25
B. The interval (2.55,3.15) is the 95% interval and (2.45,3.25) is the 90% interval-a higher level of confidence resuits in a narrower confic interval.
C. The interval (2.45,3.25) is the 95% interval and (2.55,3.15) is the 90% interval-a higher level of confidence results in a wider confiden
D. The interval (2.45,3.25) is the 95% interval and (2.55,3.15) is the 90% interval-95\% of the data points fall between 2.45 and 3.25 .
b. The 95% interval with n=140 will be than the interval with n=35 because a larger sample size provides a standard errc means a margin of error at the lence. narrower wider In finding a contidence interval for a random sample of 35 students' GPAs, one interval was (2.45,3.25) and the other was (2.55,3.15) a. One of them is a 95% interval and one is a 90% interval. Which is which, and how do you know?
b. If we used a larger sample size (n=140 instead of n=35, would the 95% interval be wider or narrower than the one reported here?
a. Choose the correct answer below.
A. The interval (2.55,3.15) is the 95% interval and (2.45,3.25) is the 90% interval-90\% of the data points fall between 2.45 and 3.25 B. The interval (2.55,3.15) is the 95% interval and (2.45,3.25) is the 90% interval-a higher level of confidence results in a narrower canfidence interval.
C. The interval (2.45,3.25) is the 95% interval and (2.55,3.15) is the 90% interval-a higher level of confidence results in a wider confidence interval
D. The interval (2.45,3.25) is the .95% interval and (2.55,3.15) is the 90% interval- 95% of the data points fall between 2.45 and 3.25 .
b. The 95% interval with n=140 will be than the interval with n=35 because a larger sample size provides a standard error, and this means a margin of error at the same level of confidence.

Answer 1

The (2.45,3.25) interval is the 95% confidence interval and is wider due to a higher level of confidence. The (2.55,3.15) is the 90% interval. If sample size increases to 140, the 95% interval will be narrower because of the reduced standard error.

Step-by-step explanation:

In finding a confidence interval for a random sample of 35 students' GPAs, where one interval is (2.45,3.25) and the other is (2.55,3.15), we must identify which is the 95% interval and which is the 90% interval, as well as understanding the effects of sample size on the width of a confidence interval.

The correct answer is C. The interval (2.45,3.25) is the 95% confidence interval and (2.55,3.15) is the 90% interval since a higher level of confidence results in a wider confidence interval. This is because more certainty requires capturing a larger proportion of the data's potential variability, leading to a broader range of values.

For part b, the answer is that the 95% interval with n=140 will be narrower than the interval with n=35 because a larger sample size decreases the standard error, leading to a smaller margin of error at the same level of confidence.