After the active learning or passive learning class, students rated the extent to which they agreed with the statement “I feel like I learned a great deal from this class.” Ratings were on a 5-point scale with greater numbers indicating greater agreement. For the 142 students in the active learning environment, the mean rating was 3.338 with a standard deviation of 0.922. For the 154 students in the passive learning lecture, the mean rating was 3.753 with a standard deviation of 0.873. Test whether ratings on feelings of learning are significantly lower, on average, with active learning. Test Statistic? P-Value ? What do you conclude?   Do not reject H0. We have evidence that mean feelings of learning are lower with active learning. Reject H0. We do not have evidence that mean feelings of learning are lower with active learning. Do not reject H0. We do not have evidence that mean feelings of learning are lower with active learning. Reject H0. We have evidence that mean feelings of learning are lower with active learning.

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 + ...