You Measure the Lifetime of a Random Sample of 25 $\sigma$

Multiple Choice

You measure the lifetime of a random sample of 25 rats that are exposed to 10 Sv of radiation (the equivalent of 1000 REM) , for which the LD₁₀₀ is 14 days. The sample mean is x?= 13.8 days. Suppose that the lifetimes for this level of exposure follow a Normal distribution, with unknown mean ? and standard deviation ?= 0.75 day. Suppose you had measured the lifetimes of a random sample of 100 rats rather than 25. Which of the following statements is TRUE?

A) The margin of error for the 95% confidence interval would increase.
B) The margin of error for the 95% confidence interval would decrease.
C) The margin of error for the 95% confidence interval would stay the same since the level of confidence has not changed.
D) The standard deviation $\sigma$ would decrease.