You measure the lifetime of a random sample of 25 rats that are exposed to 10 Sv

Question

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 = 13.8 days. Suppose that the lifetimes for this level of exposure follow a Normal distribution with unknown mean ? and standard deviation ? = 0.75 days.

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 our 95% confidence interval would decrease. B) The margin of error for our 95% confidence interval would increase. C) ? would decrease. D) The margin of error for our 95% confidence interval would stay the same since the level of confidence has not changed.

Explanation / Answer

WITH 25

Z= 1.96

ERROR = 1.96* ( 0.75 / SRQT(25) ) = 0.294

WITH 100

ERROR = 1.96* ( 0.75 / SRQT(25) ) =0.147

SO AS YOU CAN SEE THE ERROR WITH SAMPLE 100 IS LESS THAN THE ERROR WITH SAMPLE 25

A) The margin of error for our 95% confidence interval would decrease.

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