Answered: It is believed that the average amount…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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It is believed that the average amount of money spent per U.S. household per week on food is about $97, with standard deviation $12. A random sample of 25 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. State the null and alternative hypotheses for this test, the test statistic and determine if the results significant at the 5% level.

a) H_o: μ = 97, H_a: μ > 97; z = 1.250; Yes, we should reject H_o.

b) H_o: μ = 97, H_a: μ ≠ 97; z = 0.125; No, we should fail to reject H_o.

c) H_o: μ = 97, H_a: μ < 97; z = -0.125; Yes, we should reject H_o.

d) H_o: μ = 97, H_a: μ > 97; z = 1.250; No, we should fail to reject H_o.

e) H_o: μ = 97, H_a: μ ≠ 97; z = -1.250; No, we should fail to reject H_o.

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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