A food company is developing a low-calorie granola bar, and the company is interested in whether the appeal of the packaging design for the new product is related to a person's gender. There were 100 male and 100 female volunteers available for purposes of evaluation. Both males and females rated the design on a scale of 1 to 10, with 1 being “very unappealing” and 10 being “very appealing.” The mean rating for males was = 7.4, with a standard deviation = 1.5. The mean rating for females was = 8.0, with a standard deviation = 2.0. Let μ1 and μ2represent the mean ratings we would observe for the populations of males and females, respectively, and assume our samples can be regarded as samples from these populations. Reference: Ref 18-7 The degrees of freedom for these t procedures are closest to

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 + ...