Answered: 3. Following are prices, in dollars, of…

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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Question

3. Following are prices, in dollars, of a random sample of ten refrigerators:
314 377 330 285 319 274 332 350 299 306
(Note that this data is not skewed and it is reasonable to perform a hypothesis test.)
(a) Find the sample mean, x, for this data set.
(b) Find the sample variance, s2, for this data set and use it to find the sample standard
deviation, s, for this data set.
(c) A consumer organization reports that the mean price of refrigerators is greater than
$300. Do the data provide convincing evidence of this claim? Use the α = 0.01 level of
significance to conduct this hypothesis test.

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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