A researcher is investigating if adults who smoke more than 2 packs a day get fewer hours of sleep compared to other adults who do not smoke often. He collected a random sample of 35 smokers. The mean of this sample was 10.5 On average, adults that do not smoke often get 12 hours of sleep with a standard deviation of 3 and the distribution is normal. a. With alpha level of 0.01, should the researcher reject the null hypothesis? Why / why not? b. One of the researcher’s colleagues belongs to a very big family. He advised our researcher to collect data for all smokers in the family to save time and speed up the data collection process. Do you think the researcher should follow this advice? Why / why not?

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 + ...