Q.78 - The Practice of Statistics for AP

Question

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of $24$ laboratory rats. A $95\%$ confidence interval for the mean blood cholesterol level $M$ is $80.2$ to $89.8$. Which of the following would cause the most worry about the validity of this interval?

(a) There is a clear outlier in the data. 

(b) A stemplot of the data shows a mild right skew. 

(c) You do not know the population standard deviation $S$. 

(d) The population distribution is not exactly Normal. 

(e) None of these would be a problem because the t procedures are robust. 

Step-by-Step Solution

Answer

The correct option is (a).

Step 1: Given Information

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of $24$ laboratory rats. 

Step 2: Explanation

If the population standard deviation is unknown, then it is assuming in the t-procedure. But the drawbacks of the t-procedure are various outliers and skewness. Thus, there will be a clear outlier in the data in the confidence interval.

Hence the correct option is (a).