The data in the table below are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 2 7 3 18 4 7 5 6 Construct a 95% confidence interval for the true mean number of colors on national flags. Using the same x, s, and level of confidence, suppose that n were 69 instead of 39. Would the error bound become larger or smaller? How do you know? O The error bound increases because as sample sizes increase, variability decreases and we need less interval length to capture the true mean. O The error bound decreases because as sample sizes increase, variability decreases and we need less interval length to capture the true mean. O The error bound decreases because as sample sizes increase, variability increases and we need more interval length to capture the true mean. O The error bound increases because as sample sizes increase, variability increases and we need more interval length to capture the true mean. O The error bound increases because as sample sizes decrease, variability increases and we need more interval length to capture the true mean