Oral N-acetylcysteine (NAC) exerts a beneficial action in chronic bronchitis by reducing the number of exacerbations. Bontognali et al. [1] conducted a randomized, double-blind study to measure the effectiveness of NAC in the long-term treatment of patients with chronic bronchitis and mild airway obstruction. The response is the number of acute exacerbations per month. The mean value and standard deviation for both experimental and placebo group are given below: Sample size Placebo Mean Sample size 59 Standard Deviation 0.15 Standard Deviation 0.19 70 0.16 To test if there is a statistically significant differences between NAC and placebo in number of observed exacerbations, the author plans to conduct a hypothesis testing at 10% level of significance. Answer the following questions according to the study: NAC Mean 0.11

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...