Napkins IV: Drawing a Conclusion Let's finish up the napkins example. Again, here is the output: ## ## ## 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 Recall that the Research Question was: Who uses more napkins at lunch, on average: a GC male or a GC female? Which of the following is the best way to use the confidence interval to answer the Research Question? 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. ( ) If the two sexes used the same number of napkins on average, then the difference in means mu1 - mu2 would be 0. All of the values in the 95% confidence interval lie above 0, so we are quite confident, based on the data, that mu1 is bigger than mu2, which means that on average GC guys use more napkins than GC gals do. ( ) Guys use more napkins than gals do, because the interval lies above 0.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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Napkins IV: Drawing a Conclusion

Let's finish up the napkins example. Again, here is the output:

##
##
## 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

Recall that the Research Question was:

Who uses more napkins at lunch, on average: a GC male or a GC female?

Which of the following is the best way to use the confidence interval to answer the Research Question?

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.

( ) If the two sexes used the same number of napkins on average, then the difference in means mu1 - mu2 would be 0. All of the values in the 95% confidence interval lie above 0, so we are quite confident, based on the data, that mu1 is bigger than mu2, which means that on average GC guys use more napkins than GC gals do.

( ) Guys use more napkins than gals do, because the interval lies above 0.

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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