A certain herbal remedy being tested may be effective in increasing the life expectancy in people who have a rare disease. A control group consists of 25 subjects who have not taken the remedy and have a mean life expectancy of 72.1 years. A treatment group of the same size that has been given the remedy has a mean life expectancy of 79.5 years. After rerandomizing through simulation, the distribution plot for the differences of means was created and is shown below. Dot plot titled Effectiveness of Herbal Remedy with x axis labeled Difference of Means and ranges from negative 20 to 30 and y axis labeled Frequency. The low value is negative 18 and the high value is 25.

Hint: SD equals start fraction X sub H minus X sub L over six end fraction comma where SD is the standard deviation, XH is the high value, and XL is the low value

Hint: ME equals plus or minus two times start fraction SD over square root of N end square root end fraction comma where SD is the standard deviation and N is the sample size

Using N = 50, what is the margin of error (ME), rounded to the nearest hundredth, and is the naturopathic remedy effective in increasing the life expectancy of people with this rare disease?

ME = ±2.87 and yes, the remedy is effective in increasing the life expectancy in people because the original difference of means of 7.4 years is beyond, statistically, what we would expect if the differences were random
ME = ±2.03 and yes, the remedy is effective in increasing the life expectancy in people because the original difference of means of 7.4 years is beyond, statistically, what we would expect if the differences were random
ME = ±8.11 and no, the remedy is not effective in increasing the life expectancy in people because the original difference of means of 7.4 years is within, statistically, what we would expect if the differences were random
ME = ±5.74 and no, the remedy is not effective in increasing the life expectancy in people because the original difference of means of 7.4 years is within, statistically, what we would expect if the differences were random