Elementary Statistics. Need Help!

I am totally lost on this...

Suppose there is a population of test scores on a large, standardized exam for which the mean and standard deviation are unknown. Two different random samples of 50 data values are taken from the population. One sample has a larger sample standard deviation(SD) than the other. Each of the samples is used to construct a 95% confidence interval. How do you think these two confidence intervals would compare?

a. The two samples would produce identical values for the lower and upper bounds of the two confidence intervals.

b. The confidence interval based on the sample with the larger standard deviation would be wider.

c. The confidence interval based on the sample with the smaller standard deviation would be wider.

d. The two confidence intervals would have the same width because they are both 95% intervals.

Explain your choice.

b. If the data is more spread out then we can not be as certain that the mean of the population is very close to the mean of the data thus the interval is wider to allow for this. When the data has a lower deviation, most pieces of data fall close to the mean of the data so we can be more certain that the mean of the population is close to this, and the interval need not be as wide.