Question

Data on the blood cholesterol levels of 24 rats (in milligrams per deciliter) give x = 85 and s = 12. Which of the following would be most worrisome for the validity of a 99% confidence interval for the mean blood cholesterol of rats calculated from this information?
a. the presence of a clear outlier in the raw dataa
b. mild skew in the stemplot of the raw data
c. not knowing the population standard deviation Ï

Answer 1

Answer:

Option B is correct.

A mild skew in the stemplot of the raw data is the statement that makes the confidence interval obtained the most invalid.

Step-by-step explanation:

The conditions necessary for the calculated confidence interval to be valid is that the sample to be used must have been obtained using random sampling techniques with each variable independent from one another and it should be obtained from a population distribution that is normal or almost normal.

Examining the statements given to check which one of them makes the confidence interval the most invalid.

a. the presence of a clear outlier in the raw data

Only one outlier in the raw data doesn't mean that the raw data is still not almost normal. The entire distribution can still be normal with the outlier the only exception. So only one clear outlier doesn't do enough to invalidate the confidence interval obtained.

b. mild skew in the stemplot of the raw data

A mild skew in the stemplot of the raw data translates to a distribution that deviates from normality. Although, the fact that the skew in the distribution of raw data was stressed to be 'mild' indicates that the distribution can still be almost normal and still give a confidence interval that works, but of the 3 options provided, this is the one that most invalidates any confidence interval that might be obtained using these given statements.

c. not knowing the population standard deviation.

This is the least severe option, as long as the conditions given above have been satisfied, if the population distribution isn't known, the critical value that is needed to estimate the confidence interval is simply obtained from the t-distribution. The z-distribution is used when the population standard deviation is known or when the population standard deviation is not known, but the sample size is large enough to replicate the population.

So, the t-distribution ensures that we still obtain a valid enough confidence interval.

Hope this Helps!!!