Answered: An agriculture publication claims that…

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 13PPS

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Question

An agriculture publication claims that the population mean of the birth weights for all Nubian goats is

2.76

. A veterinary service has hired you to test that claim. To do so, you select a random sample of

Nubian goats and record the birth weights. Assume it is known that the population standard deviation of the birth weights of Nubian goats is

1.36

Based on your sample, follow the steps below to construct a

99%

confidence interval for the population mean of the birth weights for all Nubian goats. Then state whether the confidence interval you construct contradicts the publication's claim. (If necessary, consult a list of formulas.)

(a)Click on "Take Sample" to see the results from your random sample of

Nubian goats.

Take Sample

Number of goats	Sample mean	Sample standard deviation
35	4.62	1.27

Population standard deviation
1.36

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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