Answered: A farmer wants to know whether or not…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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A farmer wants to know whether or not the sizes of Christmas trees differ between two separate fields on opposite sides of the farm (different elevation). In order to test this, he plants a number of trees in each field and measures them all after 2.5 years of growth. He then takes a random sample from each field and this is what he found:

Group 1: Higher Elevation, N=25, Mean=3.3 ft, S=0.55 ft

Group 2: Lower Elevation, N=23, Mean= 3.1, S=0.45 ft

Please calculate the test statistic and pvalue.
- What can be concluded? Support your answer.
Please calculate the 95% confidence interval
- Interpret the interval.
- What can be concluded? Support your answer.

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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