Question

Distributions: Larger samples. In the setting of the pre- vious exercise, how many seniors must you sample to cut the range of values of x in half. This will also cut the mar gin of error of a confidence interval for u in half. Do you expect the range of individual scores in the new sample to also be much less than in a sample of size 100? Why?

Answer 1

When trying to cut the range of values of x in half, you need to sample four times as many seniors. The margin of error of a confidence interval for u is also cut in half when the sample size is doubled. No, the range of individual scores in the new sample would not be much less than in a sample of size 100.

Step-by-step explanation:

When trying to cut the range of values of x in half, you need to sample four times as many seniors. This is because the range is directly proportional to the square root of the sample size. If the sample size is doubled, the range will be cut in half.

Therefore, you would need to sample 4 times as many seniors to achieve this.

The margin of error of a confidence interval for u is also cut in half when the sample size is doubled. This is because the margin of error is inversely proportional to the square root of the sample size. If the sample size is doubled, the margin of error is halved.

No, the range of individual scores in the new sample would not be much less than in a sample of size 100. The range of individual scores is mainly dependent on the variability of the population, not the sample size. Therefore, the range of individual scores would likely remain similar regardless of the sample size.