Answered: .) The breaking strengths of cables…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

1.)

The breaking strengths of cables produced by a certain manufacturer have a standard deviation of

pounds. A random sample of

newly manufactured cables has a mean breaking strength of

1750

pounds. Based on this sample, find a

90%

confidence interval for the true mean breaking strength of all cables produced by this manufacturer. Then give its lower limit and upper limit.

2.)

A veterinary service has hired you to estimate the population mean of the birth weights for all Alpine goats. To do so, you select a random sample of

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

1.36

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

90%

confidence interval for the population mean of the birth weights for all Alpine goats. (If necessary, consult a list of formulas.)

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

Alpine goats.

Take Sample

Number of goats	Sample mean	Sample standard deviation
35	2.35	1.22

Population standard deviation
1.36

3.)

A veterinary service has hired you to estimate the population mean of the birth weights for all Alpine goats. To do so, you select a random sample of

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

1.36

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

90%

confidence interval for the population mean of the birth weights for all Alpine goats. (If necessary, consult a list of formulas.)

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

Alpine goats.

Take Sample

Number of goats	Sample mean	Sample standard deviation
35	2.35	1.22

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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