Napkins III: Interval and Interpretation

We continue with the napkins study.

The researchers have made the confidence interval:

##
##
## Inferential Procedures for the Difference of Two Means mu1-mu2:
## (Welch's Approximation Used for Degrees of Freedom)
##   napkins grouped by sex
##
##
## Descriptive Results:
##
##   group mean    sd n
##    male 3.628 2.381 43
## female 2.279 1.453 43
##
##
## Inferential Results:
##
## Estimate of mu1-mu2: 1.349
## SE(x1.bar - x2.bar): 0.4253
##
## 95% Confidence Interval for mu1-mu2:
##
##           lower.bound         upper.bound
##           0.500453            2.197222

Find the interval in the output above and say which of the following statements provide the best interpretations of it:

Group of answer choices

( ) We are 95% confident that the mean number of napkins used at lunch by all GC males exceeds the mean number used by all GC females, by an amount that is somewhere between 0.5 and 2.2 napkins.

( ) There is about a 95% chance that the mean number of napkins used at lunch by all GC males exceeds the mean number used by all GC females, by an amount that is somewhere between 0.5 and 2.2 napkins.

( ) If you look at all pairs of (one GC male and one GC female), you would find that in about 95% of those pairs the male uses between 0.5 and 2.2 more (i.e. 1 or 2 more) napkins than the female does.

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 + ...

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