Example: Assume that IRS records indicate that the mean charitable contribution on federal tax returns was $1075 in 2001. Assume a sample of April 2004 tax returns will be used to conduct a hypothesis test designed to determine whether any change has occurred in the mean charitable contributions.Formulate the null and alternative hypotheses.Assume that a sample of 200 tax returns has a sample mean of $1160 and historical records indicate that the population standard deviation s=$840. What is the value of the test statistic?What is the p-value?Using a = .05, what is your conclusion?Repeat the hypothesis test using the critical value approach.

Hypotheses: Null hypothesis: H0 : µ = 1075. That is, the mean charitable contribution on April 2004…

Answered: Example: Assume that IRS records…

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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Example: Assume that IRS records indicate that the mean charitable contribution on federal tax returns was $1075 in 2001. Assume a sample of April 2004 tax returns will be used to conduct a hypothesis test designed to determine whether any change has occurred in the mean charitable contributions.

Formulate the null and alternative hypotheses.
Assume that a sample of 200 tax returns has a sample mean of $1160 and historical records indicate that the population standard deviation s=$840. What is the value of the test statistic?
What is the p-value?
Using a = .05, what is your conclusion?
Repeat the hypothesis test using the critical value approach.

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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