Tyler and Jack are both studying a numerical variable X. Both students want to estimate the population mean of this variable, and they each intend to collect a sample, calculate a sample mean and construct a 95% confidence interval. Each student will collect their own sample, but both samples will have 30 items in them.

When constructing his confidence interval, Tyler assumes a value for the population standard deviation, . In contrast, Jack does not assume a value for the population standard deviation. Jack calculates the sample standard deviation, s, and uses this in his confidence interval. As it turns out, the sample standard deviation that Jack calculates turns out to be slightly less than the value assumed by Tyler for the population standard deviation. Based on this information, it is true to say that:

1) both confidence intervals will be of the same width

2) it is impossible to tell which confidence interval will be wider

3) Tyler's confidence interval will be wider than Jack's

4) Jack's confidence interval will be wider than Tyler's