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Name: A rods manufacturer makes rods with a length that is supposed to be 14
Uploaded: 2024-03-20T07:07:12.000Z
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Description: A rods manufacturer makes rods with a length that is supposed to be 14 inches. A quality control technician sampled 34 rods and found that the sample mean length was 14.07 inches and the sample standard deviation was 0.18 inches. The technician claim

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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A rods manufacturer makes rods with a length that is supposed to be 14 inches. A quality control technician sampled 34 rods and found that the sample mean length was 14.07 inches and the sample standard deviation was 0.18 inches. The technician claims that the mean rod length is less than 14 inches.

What type of hypothesis test should be performed?

Left-tailed t-test

Right-tailed z-test

Right-tailed t-test

Left-tailed z-test

What is the test statistic?

What is the number of degrees of freedom?

Does sufficient evidence exist at the α=0.01 significance level to support the technician's claim? Yes or No

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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