Final answer:
Using sample standard deviation in place of unknown population standard deviation leads to a wider confidence interval due to the added uncertainty and variability, especially with smaller sample sizes.
Step-by-step explanation:
When the population standard deviation is not known, and the sample standard deviation is used as an estimate, the consequence is that the confidence interval widens. This widening is due to increased variability that can be expected from smaller samples, leading to a less precise estimate of the population standard deviation. To account for this increased variability when estimating confidence intervals, we substitute the sample standard deviation for the population standard deviation and use the t-distribution, which has wider tails than the normal distribution. This substitution results in a larger margin of error for the estimation, especially notable with smaller sample sizes, and therefore the confidence interval broadens to ensure capturing the true population mean with a specified level of confidence.
In summary, using a sample standard deviation instead of the true population standard deviation generally results in a wider confidence interval, assuming all other factors remain unchanged. This makes sense because we must compensate for the additional uncertainty introduced by estimating the population parameter.