Performing Hypothesis Testing on Paired t-Test (Difference of 2 Means) Exercise A: A hog raiser in a certain province uses two meth ods of pig-farming: intensive pig farming,where pigs are housedindoorsin group-housing or straw-lin essheds; andextensive pigfarming, wherepigs are allowed to wander around the farm or fence. Test the hypothesis wheth er or not the meanweight of pigs in intensive farmingis better th an the extensive farming based from the mean weight ofthe pigs in the sample with data shown below. Use a one-tailed test at a = 1%.Inten sive farming: X, = 85 kg, si = 10 kg, and n = 55Extensive farming: X, = 79 kg, s = 6 kg, and n, = 45 Exercise B: The sample uric acid levels of selected basketball and tennis players of the same age andgen der in a certain university were tested. The result is shown below. Is there a differen ce in the meanuric acid levels between basketball and tennis players? Use a = 0.05.GroupSampleMeanStan dard DeviationBasketball players154.51.0Tennis players153.41.5

Name: Performing Hypothesis Testing on Paired t-Test (Difference of 2 Means)
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Description: Performing Hypothesis Testing on Paired t-Test (Difference of 2 Means) Exercise A: A hog raiser in a certain province uses two meth ods of pig-farming: intensive pig farming,where pigs are housedindoorsin group-housing or straw-lin essheds; andextens

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Performing Hypothesis Testing on Paired t-Test (Difference of 2 Means)

Exercise A: A hog raiser in a certain province uses two meth ods of pig-farming: intensive pig farming,
where pigs are housedindoorsin group-housing or straw-lin essheds; andextensive pigfarming, where
pigs are allowed to wander around the farm or fence. Test the hypothesis wheth er or not the mean
weight of pigs in intensive farmingis better th an the extensive farming based from the mean weight of
the pigs in the sample with data shown below. Use a one-tailed test at a = 1%.
Inten sive farming: X, = 85 kg, si = 10 kg, and n = 55
Extensive farming: X, = 79 kg, s = 6 kg, and n, = 45

Exercise B: The sample uric acid levels of selected basketball and tennis players of the same age and
gen der in a certain university were tested. The result is shown below. Is there a differen ce in the mean
uric acid levels between basketball and tennis players? Use a = 0.05.
Group
Sample
Mean
Stan dard Deviation
Basketball players
15
4.5
1.0
Tennis players
15
3.4
1.5

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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