Question

Martha Stewart has developed a new perfume. She decides to test its side effects by spraying the perfume in 31 randomly chosen houses. She records the level of antigens that create an allergic response. If the antigen level is high enough, the person will go into anaphylactic shock. The mean of her sample is a lot bigger than the median, but Martha hopes that a 90% confidence interval will contain zero. Her confidence interval is (0.116, 1.884). Disappointed, she offers you $144 to find an acceptable, realistic way to change the confidence interval to contain zero. What could you say to earn the money

Answer 1

To change the confidence interval to contain zero, we need to adjust the mean of the sample by finding an acceptable value that would make it equal to the median.

Step-by-step explanation:

To change the confidence interval to contain zero, we need to adjust the mean of the sample. Since the mean is a lot bigger than the median, we can decrease the mean by finding an acceptable value that would make it equal to the median. Let's say the median is M.

We can find the acceptable value A by calculating A = 2M - mean. By subtracting this value from each data point in the sample, we can create a new sample with a mean equal to the median and thereby change the confidence interval to contain zero.

By doing this, we are essentially shifting the entire data set so that the mean and the median are equal.